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Flying circus of physics

Chap 6 (optics) archived stories

Monday, February 02, 2009

Chapter 6 (optics). Here are the updates and new stories, including many video links and journal citations. Many more links (hundreds) and citations (thousands) for this chapter are available at

First, a list:
6.1 The third- and fourth-order rainbows have been photographed!
6.1  Rainbows and shotguns
6.2  Moonbows on the first date
6.5  Red dawn in Australia
6.15 Art --- Thomas Seddon, Pyramids of Gizeh
6.17  Christmas lights
6.20  Ice blink
6.23  Meridian line and obelisk in Paris church
6.23  Light beam penetrating Newgrange and MIT’s infinite corridor
6.28  Urban mirage
6.43  Earthshine

6.50  Blue Moon, from doo-wop to optical scattering
6.60  Prank with mirror reflections
6.61  Missing Moon in Munch painting
6.66  Mirror mazes and a puzzle
6.67  A laser sideshow and an unsolved math probem
6.74  Blind spots in vehicle mirrors
6.75  Two famous paintings
6.77  Sidewalk anamorphic art and a disappearing sculpture
6.77  Anamorphic art to control traffic speed
6.82  Mirrors, sunlight, and cheering up

6.84  Pub trick --- how water can hide a coin
6.85  Bathtub optics
6.86  Transparent when wet
6.89  Criss Angel magic --- walking on water
6.90  Transparent frogs

6.95  Opal coloration in a beetle
6.97  Star sapphire illusion
6.100  Seeing a shock front on an airplane wing
6.103  Solar images beneath a tree
6.106  Windshield light streaks 
6.113  Ouozo effect
6.117  Butterflies in daylight, moths in nightlight
6.119  Color-shifting paint and ink of cars and currency
6.126  Glass buildings act as plorization insect traps
6.128  Desert ant navigation
6.151  Pattern formed in the shadow of a solid ball or circular disk

New items (not in the book):
6.157  Halloween physics
6.158  White beetles
6.159  Wet tee-shirt (T-shirt) and sunburn
6.160  Glare off a printed page
6.161  Gun sights and quark transformations
6.162  Relativistic length contraction---what does it look like?
6.163  "Powers of Ten" --- the video
6.164  Audience scanning
6.165  Wooden mirrors
6.166  Pub trick -- water from nowhere
6.167  Pinhole rifle sites, pinhole glasses, and pinhole selfies
6.168  Pub trick --- optically reversing arrows
6.169  Black egg becomes glimmering

6.170  Retroreflecting antlers on reindeer

Reference style and difficulty dots
Dots · through · · ·  indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

Now for the stories:

6.1 The third- and fourth-order rainbows have been photographed!
Jearl Walker
Nov 2011  Most people have seen the first-order rainbow. Fewer people have seen the second-order rainbow. A handful of people have claimed to have seen the third-order rainbow. In fact, in the last 250 years there have been only five such claims that cannot be immediately dismissed.

Things have changed: In the last year, the third-order rainbow has been photographed on at least two occasions, and the fourth-order rainbow has also been photographed. Here is the photo by Michael Theusner of Schiffdorf, Germany, in which the third- and four-order rainbows appear side-by-side, with their colors reversed from each other. The third-order rainbow is just to the left of the very faint fourth-order rainbow, which is above the tree. A higher resolution copy of the photo is available at a link given below.

The third- and four-order rainbows have always been in the sky when the common first-order rainbow appears, but until modern digital enhancing was employed on a photograph of these rainbows, they had never been convincingly seen. But before I get to this breakthrough, let me explain how the first two rainbows are produced and why more rainbows should be expected.

Rainbows result when falling water drops spread white sunlight into its various colors, concentrating the colors in a band, the rainbow band. Since bright sunlight must illuminate the drops, rainbows are not seen when the cloud cover is extensive. Light undergoes refraction (its path is bent) when it enters and leaves a drop. The extent of refraction depends on color. For example, because the path of blue light is bent more than the path of red light, blue light and red light leave a drop at slightly different angles.

The most frequently seen rainbow involves light rays that enter a drop, reflect once from the interior surface, and then exit toward you. This rainbow, called the primary rainbow or first-order rainbow because there is only one reflection, has red higher than the blue. The second-order rainbow, which requires two internal reflections, has the opposite sequence of colors because of the different geometry of the light paths involved. Here is some illustrations from my textbook Fundamentals of Physics (Halliday, Resnick, and Walker), where I show the paths taken by sunrays when the Sun is near the horizon (the rays come in from the left side of the illustrations):

The additional reflection required for the second-order rainbow allows further spreading of the colors within each drop, which results in a wider and dimmer bow. The bow is also dimmed because some light is lost at each reflection point as it leaves the drop, leaving less light for the rainbow. So the second-order rainbow is not as commonly seen as the first-order rainbow. It is always there in the sky but might be too dim to be perceived.

All the falling, illuminated raindrops refract light and separate colors, but only those drops at certain angles happen to send the colored rays toward you. The drops creating the first-order rainbow must be about 42° from the antisolar point, which is directly opposite the Sun’s position relative to you. To find the rainbow drops, point your outstretched arm toward the antisolar point (at the shadow of your head) and then lift it upward or in some other direction by 42°. Your arm then points toward where drops would give you the first-order rainbow. The drops for the second-order rainbow will be about 51° from the antisolar point.

Since the drops must be at certain angles relative to the antisolar point, the rainbows form circular arcs around that point. From an elevated position, such as in an airplane, you might see full circles. Rainbows have no true distance from you—all drops along the proper angles (regardless of their distance from you) can contribute color. So, you cannot march to the end of a rainbow (to find a pot of gold). Also, the rainbow you see is personal; someone standing next to you sees colors from a different set of drops.

A rainbow is usually visible only in the early morning or late afternoon because during midday the antisolar point is too far below the horizon. Still, you might be able to see a rainbow if you look down on the drops from an elevated point.

The third- and fourth-order rainbows (requiring three and four internal reflections, respectively) lie in circular arcs around the Sun (rather than the antisolar point) but are too dim to be seen in the glare from that part of the sky. There are rare reports that third-order rainbows have been spotted, but the colors could have been due to ice crystals forming colorful halos rather than water drops forming rainbows. Still, under the right circumstances, perhaps the third-order rainbow was seen. (Those circumstances would require, for one thing, a dark background as provided by, say, dark storm clouds, instead of a brightly lit atmosphere.)

Here is my layout of the first 20 rainbows, again with the rays coming in from the left.

With our eyes, we have little hope of seeing any beyond the first two but you can find many of them using the setup described this month in “Article of the Month.” (You send white light into a single, hanging drop in an otherwise dark enclosure. As you move your eyes around the drop, you will see colorful spots on the drop corresponding to the rainbow angles. From an overhead perspective, here are the locations of the colored spots:

Well, all this has been my description of the higher-order rainbows ever since I first investigated them in the 1970s. But recently Raymond Lee of the United States Naval Academy and Philip Laven of Surrey, United Kingdom, theoretically demonstrated that the third-order rainbow might be just barely be perceptible under special lighting conditions (for example, a dark background) and for certain raindrop size distributions (the drops need to all be about the same size, which produces more distinct colors).

Spurred by that prospect, Michael Grossman of Kampfelbach, Germany searched for the third order rainbow. In one rainstorm, although he could not perceive the colors of the rainbow with his eyes, a digital photograph of that part of the sky revealed the colors after some processing (contrast stretching in order to enhance the contrast in the rainbow region). He, Elmar Schmidt of Heidelberg, Germany, and Alexander Haussmann of Technische Universitat Dresden have now published a paper on the image. Soon after Haussmann took his photograph, Theusner took his photograph of the third- and fourth-order rainbows (this is the photograph at the beginning of this story).

For many years I have argued that such photographs would just be impossible, but I am very pleased to be wrong about this. We finally get to see something beautiful that is normally just out of reach, hidden in the normal glare of the sky, like a rare painting secreted behind a thin veil. Can the fifth-order rainbow be photographed? It lies between the first- and second-order rainbows, in the dark region there (commonly known as Alexander’s dark band). It should be very faint, but maybe it too can be captured. I bet I know of at least two groups who will be trying to photograph it.


news release from The Optical Society of America:  

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Walker, J., "Multiple rainbows from single drops of water and other liquids," American Journal of Physics, 44, 421-433 (1976)
· Walker, J., "How to create and observe a dozen rainbows in a single drop of water" in "The Amateur Scientist," Scientific American, 237, 138-144 + 154 (July 1977)
· Walker, J., "Mysteries of rainbows, notably their rare supernumerary arcs" in "The Amateur Scientist," Scientific American, 242, 174-184 + 186 (June 1980)
··· Lock, J. A., "Theory of the observations made of high-order rainbows from a single water droplet," Applied Optics, 26, 5291-5298 (1987)
··· Grossmann, M., E. Schmidt, and A. Haussmann, “Photographic evidence for the third-order rainbow,” Applied Optics, 50, No. 28, F134-F141 (1 October 2011) available at ; Grossmann’s web site is at
··· Theusner, M., “Photographic observation of a natural fourth-order rainbow,” Applied Optics, 50, No. 28, F129-F133 (1 October 2011); the full paper and his photograph are available at Theusner’s website
··· Lee, Jr., R. L., and P. Laven, “Visibility of natural tertiary rainbows,” Applied Optics, 50, No. 28, F152-F161 (1 October 2011)

6.1 Rainbows and shotguns
Jearl Walker
May 2012  The most charming example of chromatic dispersion is a rainbow, the symbol worldwide for peace and beauty. How, then, could I possibly couple a rainbow with a 12-gauge shotgun? Well, this woman has done exactly that.


By firing the shotgun into the water, she is kicking up a nice spray into the air. Once airborne, surface tension pulls the water into spherical drops. When sunlight (which consists of all visible colors) is intercepted by a drop, some of the light refracts into the drop, reflects once from the drop’s inner surface, and then refracts out of the drop. The figure here (from my textbook Fundamentals of Physics) shows the situation when the Sun is on the horizon at the left (and thus when the rays of sunlight are horizontal).

The first refraction separates the sunlight into its component colors, and the second refraction increases the separation. (Only the red and blue rays are shown in the figure.) If many falling drops are brightly illuminated, you can see the separated colors they produce when the drops are at an angle of 42° from the direction of the antisolar point A, the point directly opposite the Sun in your view.

To locate the drops, face away from the Sun and point both arms directly away from the Sun, toward the shadow of your head. Then move your right arm directly up, directly rightward, or in any intermediate direction until the angle between your arms is 42°. If illuminated drops happen to be in the direction of your right arm, you see color in that direction.

Because any drop at an angle of 42° in any direction from A can contribute to the rainbow, the rainbow is always a 42° circular arc around A and the top of a rainbow is never more than 42° above the horizon.

When the Sun is well above the horizon, the direction of A is below the horizon, and only a shorter, lower rainbow arc is possible. In the video the shadows of the trees off to the left of the camera are fairly long, meaning that the Sun was fairly low. Still, we see much less than a half circle for the rainbow and so the Sun certainly was not on the horizon. The situation is like what I’ve drawn here.

Here is another video in which gunshots produce rainbow.

And here is an image showing a brilliant rainbow in the spray from farm equipment.

Can you tell that it is a fake? (Look at the shadow of the spray and decide where the Sun must be.)

Lastly, here is a video showing a rainbow in a lawn sprinkler, as commonly seen during summers. However, I include the video here only because of the audio commentary. That commentary is a strong argument that everyone should have a basic understanding of science.


6.2  Moonbows on the first date
Jearl Walker
June 2007  
A rainbow forms when direct sunlight illuminates airborne or falling water drops. In the common primary rainbow, the light enters a drop, reflects once, and then leaves the drop. If your eye intercepts this redirected light, the light appears to come from a direction that is angled about 42º from the direction of the point just apposite the Sun, the so-called antisolar point.

If you have trouble picturing that angle, stand in direct sunlight, point your finger toward the shadow of your head (which appears at the antisolar point), and then rotate your arm by 42º in any direction. Your finger then points toward where a drop could send you part of a rainbow. If you sweep your arm along a circular arc, keeping it at 42º from the antisolar point, you point along the circular arc of drops that can send you the rainbow colors. Thus, a rainbow is always part of a circle.

Moonlight can produce a rainbow in exactly the same way, except the bow is much fainter and is centered on the antilunar point (the point just opposite the Moon, where the moonlight produces a shadow of your head). Because it is so faint, a moonbow (as it is called) can be seen only at night and even then its colors are indistinguishable because the light does not excite the color receptors in your eye. So, a moonbow is white or silver, not colorful like the daytime displays produced by sunlight. Indeed, moonbows are so unremarkable that they are generally not noticed when they appear.

A moonbow can occur during rainfall if the falling drops are directly illuminated by moonlight. However, you have a better chance of seeing a moonbow in the spray of a waterfall on a clear night when the Moon is full (so that it is at its brightest). You can make the colors appear if you photograph the bow with a long exposure.

Moonbow spotting is a promising idea for a first date. You get to be out late at night, in moonlight, and near a waterfall, waiting for that special moment when the moonlight happens to illuminate the spray directly. All on the excuse that you are doing physics. Do I need to spell this out for you?

Moonbow photos and descriptions: Don Olson site Jia Liu photo Another Jia Liu photo

 · Humphreys, W. J., "Why we seldom see a lunar rainbow," Science, 88, 496-498 (1938). This is a classic paper by an early researcher on atmospheric optics.
· Olson, D. W., R. L. Boescher, and the Mitte Honors Students, “Moonbows over Yosemite,” Sky & Telescope, 113, No. 5, 24-29 (May 2007).

Want more references? Use the link at the top of this page.

6.5  Red dawn in Australia
Jearl Walker
Oct 2009 One morning last month, Australians woke to a strikingly red sky. Well, most dawns are red because of the way sunlight scatters from air molecules as it travels through Earth’s atmosphere. However, that particular morning, the sky was really red. In fact, there was a red tint to everything outside, and visibility was very limited. And the redness continued even after the Sun had climbed up into the sky.

The normal red of a sunrise (or sunset) is due to how the light scattering depends on the wavelength of the light. We normally see sunlight as being white because it consists of all wavelengths in the visible range, from the short wavelengths that we perceive as being blue or violet, to the long wavelengths that we perceive as being red. When the sunlight passes through air, it scatters from the air molecules into a range of angles centered on the forward direction. The light with the shorter wavelengths (blue) are scattered through a wider range than the light with the longer wavelengths (red). So, both colors are scattered in the forward direction, but the blue, being spread out more than the red, is weaker in that direction.

When the Sun is low in the sky, the sunlight must travel a relatively long distance through the atmosphere to reach you. Along the way, the blue end of the spectrum becomes weaker and weaker until the light is dominated by the red end. So, a rising sun will appear to be red, and the sky around it, which scatters the red light toward you, will also.

On that red-light day in Australia, special weather conditions kicked up a huge amount of dust off the Outback and then kept it aloft as it swept over the coastal areas. The dust particles were small enough that they scattered sunlight much as air molecules do. So, during sunrise, when the only sunlight reaching an observer was already red because of its passage through the atmosphere, it become even redder as it traveled through the airborne dust. Thus, only red light reached ground level. If the dirt that produced the dust was itself red (meaning that it absorbs the blue end of the spectrum), then the absorption could have also deepen the red of the ground-level light.

There was so much air borne dust that the cities were still bathed in red light even later in the day when the Sun was higher.

6.15 Art --- Thomas Seddon, Pyramids of Gizeh
Jearl Walker
August 2011  In his 1856 painting, Thomas Seddon shows a spectacular view of the pyramids at Gizeh, Egypt. The setting sun throws bright and dark shafts across the western sky, which is partially covered with clouds.

The dark shafts are due to sunlight being blocked by the clouds. Between them we see the bright shafts of sunlight, light that is not blocked. But why do the shafts diverge from the setting sun? After all, the Sun is so distant that sunrays are approximately parallel.

As I explain in The Flying Circus of Physics book, the shafts have a variety of names, including sunbeams, rays of Buddha, and Buddha’s fingers. They are almost parallel but appear to diverge or converge because of your perspective. (A similar illusion of convergence can be seen if you look along straight railroad tracks that extend a long distance away from you.) The shafts usually form when clouds near your view of the Sun throw their shadows across the sky. If there is only one small cloud, its shadow is a dark shaft. If the clouds are more extensive, you see bright shafts because of light sneaking through spaces in the clouds. (In some locations, shafts can form when light sneaks through mountain tops.) Some of the light then scatters to you from dust, rain, snow, aerosols, or air molecules along the light’s path; you can distinguish the bright shafts because of their contrast with the intermediate regions of shadow.

The shafts are difficult to see overhead, because in that perspective you are looking through their narrow width and therefore intercepting only a little of the scattered light. The shafts are easier to see when you look toward the Sun or the point opposite it, because then you view somewhat along their lengths. That means you intercept more of the scattered light, improving the contrast with shadows.

Similar shafts of light are commonly seen when bright, direct sunlight passes through very dusty air in a room that is otherwise dimly lit. You can see the shafts because dust scatters the light to you and because that scattered light is not lost in the normally brighter light reflected from the furnishings behind the shafts.

To see the journal references to rays of Buddha, go to
and scroll down to item
6.15 Bright and dark shafts across the sky

To see descriptions of other art works, go to
and scroll down to
6.61 Missing Moon in Munch painting
6.75 Two famous paintings


6.17  Christmas lights
Jearl Walker
December 2007
Most major cities are now lit up at night with plenty of light pollution by the countless streetlamps, security lights, and advertising displays. Most of the light is white, that is, it consists of so many colors that your visual system interprets the combination as being white. However, if you approach a city at night as you do when driving into it from a distance, the glow that hangs over the city is orange or red, not white. If there are low hanging clouds, they also have that color.

Similarly, although a Christmas tree may be decorated with a variety of colored bulbs, from a distance, the tree will seemingly have only orange or red lights. Bill Sones, who writes the very popular syndicated newspaper column “Strange but True,” once quipped that Santa Claus should see these altered colors as he flies toward a city or any outdoor Christmas tree. So, even Santa sees physics.

The color change has at least two causes. One involves the particle pollution that can hang over a city because of emissions from traffic and industries. Light that is emitted upward can be scattered in your direction by the overhanging haze of particles. The light might start out white, but its color gradually changes as it travels through the air to reach you. The reason is that air molecules more strongly scatter the blue end of the visible spectrum than the red end, and so the light headed toward you gradually loses the blue end and you receive light dominated by the red end.

Thus, you see a red haze above the city.

In addition, if the pollution particles have diameters of about 0.1 micrometer, then the light they scatter toward you may actually be reddish from the start.

The lights on a Christmas tree may have a variety of colors, but the blue and green light emitted in your direction will be reduced by the scattering the light undergoes with the air molecules along the way. If you are far enough from the tree, only dim red light reaches you.

Santa is not the most scientific person in the world, but I bet he could actually roughly judge his distance from a city or an outdoor Christmas tree by measuring the ratio of red to blue in the light he received. (Well, maybe he could if Rudolph the Red Nose Reindeer does not light up his nose to guide the way.)

· Went, F. W., "Air pollution," Scientific American, 192, 62-72 + 128 (May 1955)
· · · Middleton, W. E. K., Vision through the Atmosphere, University of Toronto Press, 1968, pages 172-173 

6.20  Ice-blink
Jearl Walker
Aug 2009  In olden days, native people living in the high northern latitudes would navigate through ice fields by using the open stretches of water. To avoid dead ends and to determine a path that would take them completely through an ice field, they often examined a map of the water stretches that appeared in the sky, an effect known as ice-blink.

The map appears in the sky because of the way that sunlight reflects from water and ice and how the reflected light could then scattered from water drops in the air. Light reflects well from ice but poorly from water. If a fog hangs over the area, the strongly reflected light from the water can scattered by the water drops in the fog. If an observer intercepts some of that bright scattered light, the observer sees a bright patch (sky-ice) in the sky over the ice. In contrast, the weakly reflected light from the water produces a dark patch (sky-water). These bright and dark patches make up a crude map that can guide an observer through the ice field.

Here is an example of ice-blink in a very old photograph, taken on the British Antarctic Expedition of 1907-1909.The ice-blink is the faint bright band that you might be able to see above and to the right of the man in the photograph.

The photograph is from the Sir Douglas Mawson collection of Antarctic photographs (

Here is a link to a modern photograph (by Dave Walsh) in which a far more distinct bright ice-blink can be seen above an iceberg. same photo

Ice-blink is still being used today but now by the pilots of ice-breaking ships trying to clear lanes of open water through an ice field for other ships to use. An ice-breaking ship can break its way through solid ice but following an existing lane of open water is a lot easier. So, the pilot of the ship (and also the pilot of any scouting helicopter from the ship) looks for ice-blink in the sky as a guide.

Ice-blink can also occur without any widespread fog if the water is relatively warm. Air currents then rise from the water, carrying water vapor upward, which can then condense out to form tiny water drops in the overlying air. This collection of drops can then scatter light reflected from the surrounding ice and water just as a fog can.

Recently, Ramon Hegedus and Gabor Horvath of Lorand Eotovos University in Budapest, Hungry, and Susanne Akesson of Lund University in Lund, Sweden, investigated the polarization of the light from the dark and bright regions of ice-blinks. The sky-water light (which reflects from the water and then scatters from airborne drops) is slightly polarized horizontally, that is, the electric fields of the light reaching an observer are oscillating horizontally. The sky-ice light (which reflects from the ice and then scatters from the airborne particles) can be also be slightly polarized, but the direction can be anything from being vertical to being horizontal. The researchers speculate that if the sky-ice light happens to be vertically polarized, then animals (perhaps birds) with polarization-sensitive vision might use the difference in the polarizations of sky-water and sky-ice in navigation over an ice field. However, they concede that the difference may be too difficult to detect visually.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Scoresby, W. A., An Account of the Arctic Regions, vol. 1, Archibald Constable & Co., Edinburgh, 1820, pages 299-300
· Stefansson, V., The Friendly Arctic, Macmillan, 1944, page 220
· Moller, F., "On the backscattering of global radiation by the sky," Tellus, 17, 350-355 (1965)
· Rozenberg, G. V., Twilight: A Study in Atmospheric Optics, Plenum Press, 1966, page 8
· Catchpole, A. J. W., and D. W. Moodie, "Multiple reflection in arctic regions," Weather, 26, 157-163 (1971)
· Greenler, R., Rainbows, Halos, and Glories, Cambridge University Press, 1980/1989, pages 136-138
·· Wendler, G., F. D. Eaton and T. Ohtake, "Multiple reflection effects on irradiance in the presence of arctic stratus clouds," Journal of Geophysical Research, 86, 2049-2057 (1981)
· Schlatter, T., "Weather Queries," Weatherwise, 35, 36-38 (1982)
·· Hegedus, R., S. Akesson, and G. Horvath, “Polarization of ‘water-skies’ above arctic open waters: how polynyas in the ice-cover can be visually detected from a distance, Journal of the Optical Society of America, 24, No. 1, 132-138 (January 2007). Abstract is available at


6.23 Meridian line and obelisk in a Paris church
Jearl Walker
June 2014   In the Paris church Saint-Sulpice, a tall obelisk stands on the left wall


and a brass strip runs from its foot and across the floor to near the right wall, ending in a plaque. In this photograph, obelisk is on the far wall and the brass strip runs from to the bottom left, under the chairs.


The floor strip marks a meridian line (north-south line) and the obelisk rises from it.

In line with the obelisk and floor strip, high on the right wall, a stained glass window illuminates the floor.

In one of the window’s panels, a metal plate blocks the light except for a small, circular opening in the plate.

The light from that opening forms a small disk of light on either the church floor or the left wall, depending on the time of the year. This astronomical device was built in the early 1700s such that the disk of light would pass over either the brass strip or the obelisk each day when the sun reaches its highest point in the sky (at solar noon).

At the winter solstice, when sun is low in the sky at its highest point, the disk of light passes over its highest point on the obelisk.

At the summer solstice, when the sun is high in the sky at its highest point, the disk passes over the plaque at the right side of the floor. At the fall and spring equinox, the disk passes over the part of the brass strip that lies just beyond the short fence that marks the alter. So, starting with the disk high on the obelisk at the winter solstice, the noon position of the disk slides down along the obelisk and then along the floor until it reaches the plaque on the summer solstice, and then the disk reverses the sliding.

6.23  Light beam penetrating Newgrange and MIT’s infinite corridor
Jearl Walker
Nov 2007 Newgrange is one of the most striking ancient structures in Europe, lies near Dublin, Ireland, and consists of a huge mound in which dirt covers an infrastructure of large stone blocks. Built by Neolithic people in about 3150 B.C., the mound has a 20 meter passageway that connects an entrance to a central burial chamber. A small opening in the rock lies between stone blocks just above the entrance. This opening, known now as the roof box, is most curious because it seems to have no purpose. Why would the ancient builders wrestle the heavy blocks into place so as to create this opening?

The purpose of the opening was discovered in 1969 when a researcher noticed that the opening faced sunrises during the winter. Moreover, as the sun rose on the morning of the winter solstice, sunlight penetrated Newgrange through the roof box and gradually crept along the passageway until it reached and illuminated the burial chamber, like something we would see in an Indiana Jones movie. Although the ancient people did not use Newgrange to make astronomical observations, the huge construction was still an astronomical instrument in that it marked the winter solstice by allowing the dead to be illuminated.

A similar penetration of sunlight along a long passageway occurs at the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts, during one late afternoon in November and another one in January, but by chance rather than design. On those certain days, sunlight enters the main entrance (77 Massachusetts Avenue) and creeps along the floor until it reaches the end of the so-called infinite corridor, some 250 meters long. Although this astronomical alignment was unknown when I was a student at MIT, I remember walking the infinite corridor on many sleepless nights when I prepared for an exam the next day. And I remembering hearing low moans as if previous students were buried nearby, having met academic death in those infamous MIT exams, for which studying seemingly had no effect.

Once the MIT alignment was discovered, the event became known as MIThenge, though MITgrange would be a more appropriate name. These days, the event is marked with reverence by current MIT students, who gather to witness the sunlight penetration while quietly chanting the traditional MIT slogan ihtfp. That slogan is a heart-felt expression of the student experience at MIT and stands for “in history, Tech finds purpose.”

Well, maybe.

Video Light from the rising sun at the winter solstice penetrates the passageway to the central chamber.

Photos Newgrange photos and information Photos and discussion of the sunbeam stream along the “infinite corridor” of MIT Discussion and calculation results for the MIT observations Boston Globe account of the MIT observations Photo of MIT observation Another photo Nice photo of the MIT observation

· Patrick, J., “Midwinter sunrise at Newgrange,” Nature, 249, 517-519 (7 June 1974)
· Ray, T. P., “The winter solstice phenomenon at Newgrange, Ireland: accident or design?” Nature, 337, 343-345 (26 January 1989)
· Fagan, B., “Neolithic Newgrange,” Archaeology, 47, No. 5, 16-17 (September-October 1994)
· MacKie, E. W., “Maeshowe and the winter solstice: ceremonial aspects of the Orkney Grooved Ware culture,” Antiquity, 71, 272, 338-359 (1997)
· Goldman, S. J., “Sun worship in Cambridge. Architectural researchers at MIT found a solar alignment that has enjoyed decades of popularity,” Sky & Telescope, 106, No. 5, 62-64 (November 2003)

6.28  Urban mirage
Jearl Walker
June 2007   The most common mirage (or least, the one everyone seems to notice the most) is the so-called oasis mirage that is seen on roads, especially blacktops. Distant sections of the road appear to be covered with pools of water. The sight is an illusion because the light you receive from such a section actually left something (perhaps the sky) a few degrees above the horizon. Such a ray of light is initially angled down toward the road and seemingly should strike it, where the light can be absorbed. However, if the road is much warmer than the air several centimeters above it, the ray can be bent so that it ends up in your direction. This bending is due to the temperature gradient in the layer of air lying on the road, that is, the variation of the temperature with height in that layer. As the ray descends into that layer, encountering progressively hotter air, the ray bends until it is parallel to the road and then it bends back up to leave the layer at a shallow angle.

In general, when you intercept light, your brain automatically tries to make sense of its origin, to bring an image of the light source up to consciousness. Usually the interpretation is easy. If a skunk stands in front of you, your brain makes the reasonable conclusion that the light you intercept originated on the skunk, and an image of the skunk is brought up to consciousness just as you back up really fast. But in the case of a light ray bent by the temperature gradient on a road, the best your brain can do is to conclude that the ray originated on the road. So, that section of the road seems to be shinny, as if it holds a pool of water that reflects sunlight to you.

Because the lower hot air is lighter than the higher cooler air, the hot air tends to rise but the motion is turbulent, which alters the way the light rays bend through the temperature gradient. You see the effect as shimmy in the apparent pool of water, giving the illusion that ripples driven by a breeze play over the pool. Although the pool is probably not blue because the low portion of the sky is usually whitish or only pale blue, the illusion of water lying on the road is strong.

You can also see the same type of mirage at night but without the illusion of water. When a car approaches you along a reasonably dark road, look at the display of lights on the road just in front of the car. Generally you can see a dully lit region in front of each headlight but sometimes you also see a fairly brightly lit region. The dully lit region is where light from the headlight scatters from the road. Most of the light is either absorbed or scattered into many directions, and only a little of the light ends up traveling to you.

However, you might also see a brightly lit region in front of a headlight. That light is due to the oasis mirage effect, except that here the light originates in the headlight and not in the low sky. The region is brightly lit because the light never reaches the road and thus is not dimmed by absorption or wild scattering.

There is yet another way you can see a mirage, but this one is strange. Find a wall that is warmed by direct sunlight and stand at one end so that you can look almost directly along the length of the wall. Have a friend stand at the opposite end. If you look closely, you can see a mirage of your friend seemingly just inside the wall, at the far end. The mirage is much easier to see if you look through a telephoto lens or binoculars, so that the image is expanded. This time the temperature gradient is horizontal and extending from the hot wall instead of vertical and extending from a hot road.

If you have a camera with a telephoto lens, you might consider collecting photos of urban mirage on roads, walls, and other surfaces (including bodies of water), and posting them. Send me a link. Some links to existing sites are given below here. The video link takes you to the Thrust SSC, the car that set the land-speed record as it raced over the desert at Black Rock Desert of Nevada. (The car was supersonic.) Look at the mirage under the car. 
Some of the references for urban mirage (more are listed in the pdf files)

Kosa, T., and P. Palffy-Muhoray, “Mirage mirror on the wall,” American Journal of Physics, 68, No. 12, 1120-1122 (December 2000). Video of the supersonic car Thrust SSC. Note the mirage due to the light coming across the desert ground. Photo of a wall mirage Oasis mirage on a hot road Oasis mirage on a hot road.

· Vollmer, M., and R. Tammer, “Laboratory experiments in atmospheric optics,” Applied Optics, 37, No. 9, 1557-1568 (March 1998)
· Lehn, W. H., “Bright superior mirages,” Applied Optics, 42, No. 3, 390-393 (20 January 2003)
· · · Zhao, Y., Y. Han, Z. Fan, F. Qiu, Y-C. Kuo, A. E. Kaufman, and K. Mueller, “Visual simulation of heat shimmering and mirage,” IEEE Transactions on Visualization and Computer Graphics, 13, No. 1, 179-189 (January/February 2007)

Want more references? Use the link at the top of this page.

6.43  Earthshine
Jearl Walker
March 2008
    The Moon is visible because some of the sunlight that illuminates it scatters (or reflects) from the lunar surface to you --- you see moonshine. However, if you are in a fairly dark area (away from common light pollution), you can see more of the Moon. For example, during the quarter moon phase, the bright side of the Moon is visible because of the scattering of sunlight to you, but you can also see (albeit, dimly) the dark side of the Moon. Here are several examples:

What produces that light from the “dark side of the Moon” (as Pink Floyd once put it)?

The light comes from the Earth. Although you may be on the night side of the Earth, the atmosphere on the day side is strongly illuminated and scatters some of the sunlight into space. The Moon intercepts part of the scattered light and then re-scatters. You intercept a portion of that re-scattered light --- you see earthshine. The light is dim, of course, because of all the scattering and spreading, but it is enough for you to perceive the dark side of the Moon.

Because earthshine first scatters from the atmosphere, researchers can use it as a monitor of the atmosphere. However, it also scatters from the lunar surface, which modifies the light. To subtract out that secondary scattering, researchers record both the incoming moonshine and earthshine and subtract the former from the latter. Before satellite observations of the atmosphere were available, this was about the only way someone could monitor the state of the atmosphere as a whole.

· · Goode, P. R., J. Qiu, V. Yurchyshyn, J. Hickey, M-C. Chu, E. Kolbe, C. T. Brown, and S. E. Koonin, “Earthshine observations of the Earth’s reflectance,” Geophysical Research Letters, 28, No. 9, 1671-1674 (1 May 2001)
· Woolf, N. J., P. S. Smith, W. A. Traub, and K. W. Jucks, “The spectrum of earthshine: a pale blue dot observed from the ground,” Astrophysical Journal, 574, 430-433 (20 July 2002)
· · Montanes Rodriguez, P., E. Palle, P. R. Goode, J. Hickey, J. Qiu, V. Yurchyshyn, M. C. Chu, E. Kolbe, C. T. Brown, and S. E. Koonin, “The earthshine spectrum,” Advances in Space Research, 34, 293-296 (2004)
· · Montanes-Rodriguez, P., E. Palle, and P. R. Goode, “Measurements of the surface brightness of the earthshine with applications to calibrate lunar flashes,” Astronomical Journal, 134, No. 3, 1145-1149 (September 2007)
Want more references? Use the link at the top of this page.

6.50  Blue Moon, from doo-wop to optical scattering

Jearl Walker
May 2008 
   I know exactly where and when I first wondered about a blue Moon: I was at a high school dance trying to muster up the courage to talk to Marcia Sims, when someone played a record by the doo-wop group the Marcels. They sang,

“Blue moon, you saw me standin' alone
Without a dream in my heart, without a love of my own
Blue moon, you knew just what I was there for
You heard me sayin' a prayer for
Someone I really could care for”

The song, written in 1934 by Richard Rogers and Lorenz Hart, is sung by the Marcels at
and by Elvis Presley at

The Moon is white because it reflects light from the Sun, which we see as being white because it contains the full range of the visible spectrum. So, how could the Moon ever be blue as in the old song? And how about the common statement in English, that something might happen only “once in a blue Moon,” which means “very rarely”?

A blue Moon has two astronomical definitions. Commonly it refers to the second full Moon in a calendar month, a rare occurrence because a lunar cycle takes about 29.3 days, thus making it difficult to squeeze two full moons into a calendar month. This meaning appears to have begun (due to a misunderstanding) in the March 1946 issue of Sky & Telescope magazine.

An older meaning has to do with the number of lunar cycles (waxing and waning) that occur in a season. If there are four such cycles, then (for no good reason) the third cycle has been called the blue Moon. Such a blue Moon occurs this month, so get your party plans in order now, because I am sure that the nightclubs will be heavily booked because of all the excitement.

Either of these definitions dovetails neatly with the description of an event as being rare. That meaning of rarity seems to have first appeared in 1528 when the idea of the Moon being blue was used to characterize an impossible event.

So, what did Rodgers and Hart mean in their very popular song? They wrote the lyrics long before the phrase meant two moons in a month, and the idea of a rare event makes little sense in the lyrics. Thus, they must have just being using a cute phrase to describe a full moon looking down on a lonely person, with the word “blue” referring to the sad state of the person.

However, there is another meaning to blue Moon because there are times when the Moon really does look blue. Oh, I don’t mean that someone on the lunar surface would have seen anything but white light. I mean that at times the Moon can appear to be blue when seen through Earth’s atmosphere.

One such time can occur when you see the Moon surrounded by dimly lit orange and purple clouds, as can occur during sunset or sunrise. Then, in what is called a contrast illusion, the white of the Moon may seem to have a blue tint in contrast to the dominant red you receive from the clouds. (Red and blue are at opposite ends of the visible spectrum.) This explanation of a blue Moon was offered by Marcel Minnaert, the father of atmospheric optics and the author of one of the best popular physics books ever written, Light and Colour in the Open Air, a book that propelled me into writing The Flying Circus of Physics. The blueness, however, is an artifact of your visual system and would not be detected by, say, a camera.

Well, an illusion is just an illusion, of course, and not reality. Is there anytime that even a camera would record the Moon as being blue. Yes, on several occasions, the Moon has been colored by large-scale aerosols thrown up into the atmosphere by volcanoes or large forest fires. The blue coloration occurs when the aerosols consist of particles with radii of about 0.4 to 0.9 micrometer (micron). When white light from the Moon passes through an aerosol with particles in that range, the red end of the visible spectrum gets more strongly scattered to the side than the blue end. Someone on the ground who looks directly at the Moon sees the end result after a lot of the red has been removed from the moonlight --- the surviving moonlight has more blue than red and thus looks blue, even to a camera.

Because seeing the Moon through such an aerosol has been very rare, perhaps that rarity initiated the original meaning of something being as rare as a blue Moon. We shall never really know.

Although “Blue Moon” by Rodgers and Hart was one of the more enduring songs ever written, I think the most haunting reference to a blue Moon occurs in the classic 1980s electro-pop song “The Killing Moon” by Echo and the Bunnymen, which got me through many long nights. Here are the opening lyrics

“Under blue moon I saw you
So soon you'll take me
Up in your arms
Too late to beg you or cancel it
Though I know it must be the killing time
Unwillingly mine”

and here are links to some of the group's performances:

By the way, I never did get up the courage to talk to Marcia Sims.

· ·
Porch, W. M., "Blue Moons and large fires," Applied Optics, 28, 1778-1784 (1989)
· Nishiyama, R. T., (letter) “Blue suns,” Weather, 48, 417 (1993)
· Greenler, R., and R. K. Brandt, “Only once in a blue moon,” Optics and Photonics News, 5, No. 10, 6-7, 66-67 (1994)
· Horvath, H., G. Metzig, O. Preining, and R. F. Pueschel, “Observation of a blue sun over New Mexico, U.S.A., on 19 Aril 1991,” Atmospheric Environment, 28, No. 4, 621-630 (1994)
· · · Stothers, R. B., “Major optical depth perturbations to the stratosphere from volcanic eruptions: pyrheliometric period, 1881-1960,” Journal of Geophysical Research, 101, No. D2, 3901-3920 (20 February 1996)
· Hiscock, P., “Once in a blue moon,” Sky & Telescope, 97, No. 3, 52-55 (March 1999)
· Lynch, D. K., and W. Livingston, Color and Light in Nature, 2nd edition, Cambridge University Press, 2001, page 149
· Wilk, S. R., “Once in a blue moon,” Optics and Photonics News, 17, 20 (March 2006)

Want more references? Use the link at the top of this page.

6.60  Prank with mirror reflections
Jearl Walker
Nov 2007 We take mirror reflections for granted but they are actually a marvel. When you see your reflection, your image appears to be an exact duplicate of you, just as far from the glass as you are. In spite of what many people think, the reflection does not give a left-right reversal because everything that is on your left appears on your left in the reflection.

You take a mirror reflection for granted so often that you probably don’t pay much attention to it and simply concentrate on whatever you are doing, such brushing your hair or tying your tie. But suppose that the reflection suddenly was not a perfect duplicate of you. How long would you take to realize something is very wrong? In fact, how long would you need to consciously know that the physics is wrong if your image disappears? Well, here is a video in which missing images befuddle several people because the suspension of physics makes their world unreal. same video but with subtitles

6.61  Missing Moon in Munch painting
Jearl Walker
June 2006
     In the painting Girls on the Pier, Edvard Munch shows two girls standing on a pier as the Moon hovers some 8º above the horizon ( Strangely, however, a reflection of the Moon does not appear in the water below the pier, whereas reflections of other things, such as a house and a tree, are there. Was Munch being careless or profound? Was there a hidden philosophical meaning behind the Moon’s lack of reflection?

     Although Munch (and the girls) could see the Moon directly, the rays of light from the Moon that should have given them a reflected image were blocked by the house they saw (directly) just below the Moon. If Munch had moved down to the point on the water where the moon rays should have been reflected and then looked up toward the Moon, he would not have seen the Moon because it would have been behind the house. So, from that viewpoint, the lack of a Moon would not have been mysterious. However, from the viewpoint up on the pier, the blockage of Moon rays by the house is not obvious and the lack of a Moon reflection seems strange.

Olson, D. W., B. Robertson, and R. L. Doescher, “Reflections on Edvard Munch’s Girls on the Pier,” Sky & Telescope, 111, No. 5, 38-41 (May 2006)

Want more references on reflections off water? Use the link at the top of this page.

6.66  Mirror mazes and a puzzle
Jearl Walker
May 2009 A mirror maze (or mirror labyrinth) is a maze where every wall is covered with a full-length mirror. Walking through such a maze can be bewildering because the multiple reflections can easily hide the correct path to take (the solution to the maze). When the floor sections form equilateral triangles (60º angles), you see either a jumble of images or virtual hallways that seemingly stretch away from you.

In this photo, which was shot in a mirror maze that stood in Lucerne, Switzerland, you can see virtual hallways stretching off to the left and right. (If you look closely between the woman and her image on the right, you can also see an almost hidden image of the photographer next to his camera, grinning with pleasure.) When I went through this maze, I repeatedly ended up walking into the mirrors because I could not distinguish a virtual hallway from the real path through the maze.

My old article about the optics of this maze and mirror mazes in general is this month’s “Article of the Month,” posted in the News/Updates. (Do you see the button in the menu at the left side of the screen?) Let me entice you to read the article by giving you a puzzle:

The figure here shows an overhead view of a mirror maze based on floor sections that are equilateral triangles, as indicated by the dashed lines in the figure.

Every wall within the maze is mirrored (on both sides), as indicated by the solid lines. You look into the maze at point x in the maze’s entrance. Three maze monsters (the kind that gobble you up if you get lost) lurk in the maze at points a, b, and c. From your viewpoint at x, which monsters are hidden from view (they do not appear in any virtual hallway that seemingly extends away from point x)? For any visible monster, how many times does it appear in one of the virtual hallways? What appears at the end of each hallway — that is, is there a monster there or something else?

You can find the answers just after the journal references for this item below. Here is a quick analysis of mirror mazes but a more thorough (yet nonmathematical) analysis can be found in my Amateur Scientist article (the first of the journal references).

Part a of the figure here shows an overhead view of a very simple mirror maze in which differently painted floor sections form equilateral triangles.

You look into the maze while standing at point O at the middle of the maze entrance. In most directions, you see a confusing jumble of images. However, you see something curious in the direction of the ray shown in part a. That ray leaves the middle of mirror B and reflects to you at the middle of mirror A. (The reflection obeys the law of reflection, with the angle of incidence and the angle of reflection both equal to 30º.)

To make sense of the origin of the ray reaching you, your brain automatically extends the ray backward. It appears to originate at a point lying behind mirror A. That is, you perceive a virtual image of B behind A, at a distance equal to the actual distance between A and B, as drawn in part b of the figure. (The image is said to be virtual because it exists only in your brain. If you held a sheet of paper at its apparent location behind the mirror, nothing would appear on the paper.) Thus, when you face into the maze in this direction, you see B along a virtual straight hallway consisting of four floor sections.

This story is incomplete, however, because the ray reaching you does not originate at mirror B — it only reflects there. To find the origin, we continue to apply the law of reflection as we work backwards, reflection by reflection on the mirrors. Working through the four reflections shown in part c, we finally come to the origin of the ray: you! What you see when you look along this virtual hallway is a virtual image of yourself, at a distance of nine triangular floor sections from you (part d of the figure). There is a second virtual hallway extending away from point O. Which way must you face to look along it, and what lies at the end of it?

You might invent your own mirror maze in which monsters can be hidden from view when you stand at certain points in the maze. Let me know what you find.

The world’s leading builder of mazes (mirror mazes, hedge mazes, and mazes of any other type) is Adrian Fisher. Here is a video in which he explains The London Dungeons mirror maze that he built in London, England. The current mirror maze in Lucerne Adrian Fisher’s web site, with lots of photos of his mazes. Maize mazes Fisher’s mirror maze in Birmingham, England Charlie Chaplin explores a mirror maze in one of his movies Amaze ‘n’ Things Mirror Maze

Photos Some of Adrian Fisher’s mirror mazes Mirror maze at Lucerne, Switzerland,_Switzerland/

· Walker, J., "Mirrors make a maze so bewildering that the explorer must rely on a map" in "The Amateur Scientist," Scientific American, 254, 120-128 + cover (June 1986)
· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, 8th edition, Wiley, 2008, pages 928, 948. The puzzle here is a figure in this book that I write.

Answers to the puzzle in the item about mirror mazes:
Monster b does not appear in a hallway stretching from the entrance.
The other monsters can be seen 3 times in a hallway.
You see yourself at the end of each hallway.

6.67  A sideshow laser shoot and an unsolved math problem
Jearl Walker
June 2015  

From the FCP book

As you stroll through a carnival’s sideshows, passing familiar games of skill and chance, you spot a new amusement, “The Laser-Blast Target Shoot.” Intrigued, you enter, finding yourself in the corner of a rectangular room with walls covered with ideally reflecting mirrors. At your corner there is a powerful laser locked into place horizontally and at an angle of 45° to the walls. At each of the other corners, a clay armadillo target smirks at you.

The attendant behind you explains that you are to shoot the laser after first guessing whether a target will be hit and, if so, which one. He also points out that the room has been precisely constructed with a length of 7 units and a width of 4 units. He then abruptly leaves, as if your corner might be the real target.

Will you hit a clay target or yourself, or will the light reflect around the room until the slight absorption at each reflection finally eliminates it? What would happen if the dimensions were 7 units and 3 units, or 8 units and 3 units? Bravely you squeeze the trigger as you try to envision the multiple reflections you are about to create.

As long as the length and width of the room are both integers, you will not shoot yourself and are sure to hit a clay target. To find out which one, you might trace the shot around a sketch of the room or you might use the following recipe. If the ratio of length to width can be reduced (for example, 8/4 can be reduced to 2/1), do so, and then consult the three possible results shown below, where the odd and even dimensions of the sides are the key.

More general

There are more general questions that are similar. If a light source is located in a polygonal room (make it just two-dimensional) with fully reflecting walls, will the source illuminate every point on the room’s wall regardless of the room’s shape? If the room is circular or square and the source is in the middle, the easier is easily yes. But if the polygon is more complicated or the room has curved walls, the answer is yes for certain shapes but no one has been able to decide for all shapes. This illumination of a room remains one of the unsolved problems in mathematics.

A related problem was posed by John E. Connett in 1992. If a beam of light is sent into the mouth of a container with a fully reflecting interior, will some of the light eventually be reflected back out through the mouth? Here is his whimsical drawing of the situation.

No one has been able to answer Connett’s question for an arbitrarily shaped container.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Himmelfarb, A., "A billiard table problem," Problem E 1879, American Mathematics Monthly, 73, 411 (1966)
·· Silverman, D. L., "A billiard table problem," Solution to Problem E 1879, American Mathematics Monthly, 74, 870 (1967)
··· Klee, V., “Is every polygonal region illuminable from some point?” The American Mathematical Monthly, 76, No. 2, 180 (February 1969)
· Grant, N., "Mathematics on a pool table," The Mathematics Teacher, 64, 255-257 (1971)
· Hamel, T. R., and E. Woodward, "Developing mathematics on a pool table," The Mathematics Teacher, 70, 154-163 (1977)
· Jacobs, H. R., Mathematics: A Human Endeavor, W. H. Freeman, 1982, pages 6-17
·· May, B. A., “Reflections on miniature golf,” Mathematics Teacher, 78, 351-353 (May 1985)
· Shultz, H. S., and R. C. Shiflett, "Mathematical billiards," Mathematical Gazette, 72, 95-97 (1988)
· Griffel, D. H., "More mathematical billiards," Mathematical Gazette, 73, 118-119 (1989)
· Connett, J. E., “Trapped reflections,” American Mathematical Monthly, 99, No. 2, 178-179 (February 1992)
·· Tokarsky, G. W., “Polygonal rooms not illuminable from every point,” American Mathematical Monthly, 102, No. 10, 867-879 (December 1995)
· “Cover activity: rational billiards,” Mathematics Teacher, 89, No. 1, pages 3 + cover + table of contents (January 1996)
··· Chernov, N., and G. Galperin, “Search light in billiard tables,” Regular and Chaotic Dynamics, 8, No. 2, 225-241 (2003)


6.74  Blind spots in vehicle mirrors
Jearl Walker
December 2013  The purpose of a vehicle’s side-view mirror is to allow you to see a trailing vehicle in an adjacent lane. However, many arrangements of a flat mirror leave a blind spot, which is a region in which the trailing vehicle is too close to be visible in the mirror. The danger is that you may switch lanes without being aware of a nearby vehicle. The vehicle might be slowly passing you (it could disappear from view for several seconds) or traveling at your speed (it is then continuously hidden from view). I have some photos to illustrate the situation but if you want something more startling (especially if you are a parent), skip to the video link farther down.

Here is a sketch of the blind spots on two sides of my car (I drive on the left side) with two flat side-view mirrors.
I can initially see an overtaking car with the rearview mirror, then eventually with a side-view mirror, and then finally with my peripheral vision as the car pulls alongside me, either in the adjacent lane or the next lane over. The danger lies in the interval when the car is no longer visible in my rearview mirror and before it is visible in my side-view mirror. If it is moving rapidly while I change lanes in its direction, there can be a collision before either the other driver or I realize my error.

I arranged two stationary cars in my driveway so that when I photographed through the rear-view mirror and through the right-hand side-view mirror of the lead car, the trailing car was not visible. Here is what I see through the rear-view mirror.

And here is what I see through the right side-view mirror.

The trailing car is not seen through either mirror. Here is the arrangement as seen in front of the cars.

While sitting in the leading car, I could, of course, turn my head sharply to look back along the adjacent region. However, taking my eyes off the road at high speed is itself dangerous. Besides, the headrests and side panels framing the rear window obscure my view, requiring a longer look for me to understand if a car is there.

A safer but simple solution is to mount the side-view mirror on the front of the car hood , as was done with some sports cars. Although this gives a much broader view of the adjacent lanes, the mirror is so far from the driver that the image is small for any reasonable size of mirror. Another solution is commonly used on trucks: A convex mirror is added to the side-view mirror to give a broad view of the adjacent lanes. Again the image is small but now the mirror is close enough to the driver to be useful.

I use a third solution. I quickly lean forward while I glance at the side-view mirror. I can then see any car in the blind spot.

The situation on my driver’s side of the car is about the same. Again I've arranged for there to be a trailing car but this time on my left side. Here is the view through the side-view mirror on the left side.

And here is the scene from in front of the cars.

Here again a car can disappear into a blind spot, but I can see it by leaning forward.

Here is a video that more dramatically demonstrates a blind spot, this time to a truck driver and in spite of the fact that the side-view mirror (on the left side on this United Kingdom truck) has a convex portion.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
·· Quadling, D., "What the eye doesn't see, ..." Mathematical Gazette, 71, 198-201 (1987)
·· Clifford, F., "More on drivers' blind spots," Mathematical Gazette, 73, 120 (1989)
· Luoma, J., M. Sivak, and M. J. Flannagan, “Effects of driver-side mirror type on lane-change accidents,” Ergonomics, 38, 1973-1978 (1995
··· Hicks, R. A., and R. K. Perline, “Blind-spot problem for motor vehicles,” Applied Optics, 44, No. 19, 3893-3897 (1 July 2005)

6.75 Two famous paintings
Jearl Walker
Dec 2010 Edouard Manet’s A Bar at the Folies-Bergere has enchanted viewers ever since it was painted in 1882.

 Part of its appeal likes in the contrast between an audience ready for entertainment and a bartender whose eyes betray her fatigue. Its appeal also depends on subtle distortions of reality that Manet hid in the painting distortions that give an eerie feel to the scene even before you recognize what is “wrong.”

The 1915 painting I am half-sick of shadows said the Lady of Shallott by John William Waterhouse is based on the 1842 poem The Lady of Shalott by Alfred, Lord Tennyson:

    But in her web she still delights
    To weave the mirror’s magic sights,
    For often thro’ the silent nights
    A funeral, with plumes and lights
    And music, went to Camelot:
    Or when the moon was overhead
    Came two young lovers lately wed:
    “I am half sick of shadows,” said The Lady of Shalott.

 When I saw the painting for the first time, my attention was first directed to the lady, who has paused in her weaving, and then to the scene outside her room. Only with study did I realize that I was looking at a circular mirror rather than through a circular window. Do you see the clues?

In A Bar at the Folies-Bergere you see the barroom via reflection by a large mirror on the wall behind the woman tending bar, but the reflection is subtly wrong in three ways. First note the bottles at the left. Manet painted their reflections in the mirror but misplaced them, painting them farther toward the front of the bar than they should be.

Now note the reflection of the woman. Since your view is from directly in front of the woman, her reflection should be behind her, with only a little of it (if any) visible to you; yet Manet painted her reflection well off to the right.

Finally, note the reflection of the man facing her. He must be you, because the reflection shows that he is directly in front of the woman, and thus he must be the viewer of the painting. You are looking into Manet’s work and seeing your reflection well off to your right. The effect is eerie because it is not what we expect from a painting or from a mirror.

In I am half-sick of shadows said the Lady of Shallott, we see the outdoor scene because of a circular mirror on the wall behind the lady. The clue lies in the reflection of the loom in the lower part of the mirror. The windows must be behind us as we look into the painting, but notice the small display of red (perhaps a red flower) that appears to be next to the reflection of the loom. We can see the red display in the reflection but not in our direct view of the loom. Either it was left out of the painting to intrigue us or it is behind us, closer to the windows.

Reflections can be interesting but are usually mundane because our subconscious takes the physics of reflection for granted. However, when something is wrong in the reflections, we can sense it even before consciously know what exactly is wrong. I am half-sick of shadows said the Lady of Shallott is currently hanging at the Art Gallery of Ontario in Toronto, Canada, and A Bar at the Folies-Bergere is currently hanging at J. Paul Getty Museum in Los Angeles. If you know of other examples where a painter has taken the advantage of this technique of capturing our attention, let me know.


6.77  Sidewalk anamorphic art and a disappearing sculpture
Jearl Walker
June 2007   Anamorphic art contains an image that may be so distorted that it is unrecognizable. However, if you take a certain perspective, perhaps a certain angle of view, the image is clearly recognizable. My favorite style of anamorphic art is where the image is recognizable only if the art is viewed via a reflection, such as from a curved mirror. A link to an example of such anamorphic art is given below.

A different style of anamorphic art is used by Julian Beever when he makes chalked drawings on sidewalks (see the other links below). When viewed at the correct angle, his two-dimensional drawings spring into three dimensions. Indeed, the Coke bottle drawing in one of the links seems to hover above the sidewalk. This is not holography. This is not Luke Skywalker viewing Princess Leia in some kind of holographic projection. This is just chalk and a finely tuned sense of humor on the part of the artist.

The quantum man sculpture by Julian Voss-Andreae, an artist with a background in physics, is a reverse sort of anamorphic art. Instead of the art making sense only in one view, it makes sense in all views except one, and in that one view the sculpture disappears.

The metal sculpture consists of many thin, parallel plates. When you stand in front of the sculpture, you see the broad faces of the plates, and their composite arrangement and shape is that of a man. However, if you stand directly to the side, so that you are looking at the thin widths of the plates, you see through the sculpture, as if it is not really there. That is, the human figure disappears, surely a stark statement about the existential nature of human life---full of meaning from some views, completely empty from other views.

Use the link below to access the web site of Voss-Andreae and the multiple views of his sculpture. Example using cylindrical mirror Amazing anamorphic sidewalk art by Julian Beever  Julian Beevar Video shows how Beever sets up the art. Another amazing sidewalk example by Julian Beever  Watch how the art comes "alive"   Beever meets the Transformers, for the new movie Video about the sidewalk art of Julian Beever  Anamorphic art on an LCD screen
Quantum man by Julian Voss-Andreae. Click on "archive"; choose "Matter Wave Project II", click on one of the slides and then use the "Next" arrow at the top to go to the next slide.

Here is an example of anamorphic art on a wall, giving the illusion of a door in the wall.

· Walker, J., "Anamorphic pictures: distorted views from which distortion can be removed" in "The Amateur Scientist," Scientific American, 245, No.1, 176-187 (July 1981)
· Falk, D. S., D. R. Brill, and D. G. Stork, Seeing the Light. Optics in Nature, Photography, Color, Vision, and Holography, Harper & Row, 1986, pages 79-83
· · Hickin, P., "Anamorphosis," Mathematical Gazette, 76, 208-221 (1992)
· · 
Hunt, J. L., B. G. Nickel, and C. Gigault, “Anamorphic images,” American Journal of Physics, 68, No. 3, 232-237 (March 2000)

Want more references? Use the link at the top of this page.

6.77  Anamorphic art to control traffic speed
Jearl Walker
Nov 2010 In West Vancouver, Canada, anamorphic art is being used to caution motorists to slow to the legal speed limit. Instead of a sign or even a speed bump, a distorted image of child playing with a ball has been painted on the road or driving lane. From overhead, the child is hardly recognizable because the proportions and shape are highly distorted. However, from the perspective of a motorist approaching the painting, the child is easily identified and appears to be real. video shot from a car moving toward and then over the anamorphic art
The motorist does not perceive the painting as being on the horizontal road. Rather the motorist perceives it as being on a vertical surface. If the painting were drawn true to size on the road, the farther part (the child’s head) would be too narrow and shallow compared to the nearer part (the child’s feet). So, the painter distorted the image by painting the farther part wider and more extended than the true proportion. The illusion is then greatly aided by the motorist’s visual system, which tries to make sense of what is being seen in terms of familiar, recognizable objects.

Anamorphic paintings on canvas or walls have been around a long time, either as novelties or as ways of criticizing a ruler without the criticism being readily apparent. In recent times, anamorphic art has made the leap from canvas to the sidewalk and streets, usually chalked in beautiful detail. My favorite such street chalk artist is Julian Beever. Here is an example with him posing in the shot to add the illusion of reality. CNBC item about street anamorphic art


To see more about pavement anamorphic art, especially the work by Julian Beever, go to and scroll down to item 6.77.


6.82  Mirrors, sunlight, and cheering up
Jearl Walker
December 2007
    Because the sun is frequently hidden by clouds during the winter here in Cleveland, Ohio, we sometimes have pretty dreary days. However things can be worse, such as in Rattenberg, Austria. That small town lies in a valley in the Alps and, more important, behind Rat Mountain which shields the town from direct sunshine during December and January each year. Although the town certainly receives indirect sunlight during those months, the continuous lack of direct sunlight can be depressing to some of the inhabitants.

To decrease that possibility and at the invitation of the town, the lighting company Bartenbach LichtLabor of Aldrans, Austria, has designed a mirror system to reflect sunlight into Rattenberg. An automatically steered mirror would be positioned on the north side of the valley to send sunlight to mirrors just above the town, on the south side of the valley. Those secondary mirrors would send the light down into the town to illuminate at least one of the two main streets. Thus physics could light up that street and possibly cheer up some of the town’s inhabitants. (Get the message here? Physics can be cheery.)

In 1993, Russia tested a similar idea in the hope of alleviating the depressing long periods of winter darkness in the towns located in the Russian high latitudes. The government orbited a plastic mirror with a 22 meter diameter. The test was to see how much sunlight the mirror could reflect down into the night side of Earth whenever the satellite was in direct sunlight while over the night side. Unfortunately, the mirror did not last very long but it did manage to produce a dim spot of light, several kilometers wide, that swept across Europe. The spot was seen by several observers, but no one claimed to have been cheered up by the experience.

In The Flying Circus of Physics book I describe my favorite Arthur C. Clarke short story in which an angry football crowd used the reflection of sunlight to show their contempt for a biased call by a referee against the home team. Each spectator had been given a special program as they entered the stadium, with one side of the program very fancy and reflective. When the referee made the biased call, every spectator whipped out the program with the reflective side facing the sun and then oriented the program so that the sunlight reflection fell on the referee. The concentrated sunlight replaced the referee with a thin trail of smoke. Obviously he was not cheered up by the experience. The company Bartenbach LichtLabor, in English. The same site but in German

· Phillips, E. A., (letter) "Arthur C. Clarke's burning glass," Applied Optics, 13, A16 + 452 (February 1974)
· Lacoste, B., “Space ‘umbrella’ lights up the Earth,” New Scientist, 136, No. 1841, 19 (3 October 1992)
· “Cosmic Klieg light,” Sky & Telescope, 85, No. 6, 13 (June 1993)

Want more references? Use the link at the top of this page.

6.84  Pub trick --- disappearing coin
Jearl Walker

April 2010
Make the coin disappear

Place a common drinking container with clear, transparent glass over a coin on a table and look through the side wall at the coin.

Then fill the glass with water. The coin is no longer visible, that is, the water somehow hides the coin.

You can also see this disappearing act in the video that is linked down below here. The question is, of course, how could water hide the coin? Water is transparent. The glass bottom is transparent. Why can’t we simply look through them at the coin as originally when the glass was empty?

Here is the original arrangement, with a dot representing the coin below the glass bottom.

Light from overhead and from the sides of the drinking glass penetrate the glass bottom and then scatter from the coin in many different directions. A few of those rays are shown leaving through the left side of the drinking glass. Where the rays enter either the bottom face or side wall, they are bent into a new direction, an effect called refraction. Because air lies on both sides of the bottom face and side wall, that redirection is reversed where the rays emerge into the air, and so the rays end up traveling in their original direction.

The speed of light through any transparent material depends on the nature of the material. However, rather than detail the material’s properties, we usually just assign an index of refraction to the material as a measure of the speed of light within it. For example, the index of vacuum is 1 (the light speed is at its greatest value c), the index of air is slightly more than 1 (the light speed is slightly less than c), the index of water is 1.33 (the light speed is even slower), and the index of glass can be around 1.5 or higher (the light speed is even slower).

Refraction (bending into a new direction of travel) occurs when light passes through an interface that separates materials with different indexes of refraction. We measure the bending by the angle the light ray makes with a line (called the normal) that is perpendicular to the interface. For example, here is the side wall when water fills the container. The light ray travels from the water side of the wall (higher index) to the air side (lower index), bends away from the normal to the interface.

An extreme case occurs when the emerging light ray is bent so much that it skims along the side wall.

If I assume that the water and glass have an effective index of 1.4 (an average of the index of water and the index of glass), then this skimming occurs when the ray on the water side is at 46º from the normal. If the angle is greater than 46º, the ray cannot pass through the surface and can only reflect inside the water. Such entrapment is called total internal reflection. Since the ray does not emerge on the air side, we don’t intercept it.

Let’s assume that the ray reaches the interface at the critical value of 46º. Then when it enters the water through the bottom face, it must have an angle of 44º with the normal there. That angle of 44ºdetermines the angle of the ray (77º) on the air side of the bottom face, and thus the angle of the ray as it leaves the dot that represents the coin.

Now here is the argument about why the coin is hidden when the drinking glass contains water. If we are to see the coin, light rays must pass through the side wall. That can happen only if they have an angle of less than 46º on the water side of the side wall. And that can happen only if they an angle of more than 44º on the water side of the bottom face. And that can happen only if they have an angle of more than 77º on the air side of the bottom face.

However, only a small amount of light leaves the coin in that angular range. And beside, with such a glancing entrance to the bottom face, the rays become distorted within the glass of the bottom face. If we intercept such dim and distorted light, we cannot form an image of the coin, and thus the coin is hidden. In some situations (with different types of glass), even such dim light may not be able to pass through the side wall.


Make the coin reappear

With water filling the drinking glass, can you make the coin reappear as seen through the side wall?

The answer is this: Pull the coin out for a moment, coat it with water, and then put it back under the glass. The light that leaves the coin passes from the water coating into the water of the glass without any bending (the slight bending by the glass face when the light enters the glass is undone when the light leaves the glass).

Let’s go through the angle argument again. In order for light to emerge through the side wall, it must have an angle of less than 46º on the water side. And that means it must have an angle of more than 44º above the bottom face. And that means that it must have an angle of more than 44º (the same angle) below the bottom face. Plenty of light leaves the coin in such an angular range, without being distorted. So, we can now see the coin through the side wall.

If you actually use this trick in a pub, you might try pale ale instead of water (it is almost the same as water and is fairly transparent)s. Then as a finale, you can do one more disappearing trick ---- you can make the ale disappear by drinking it. Ah, that’s the best part. same video


6.85  Bathtub optics
Jearl Walker
March 2008
    If you see a penguin, your brain brings up to consciousness a mental picture of the penguin by mentally extending backward the light rays you intercept from the penguin. Aided by the life-long experience of judging size and distance, you perceive the penguin at its proper size and distance.

But suppose that you are submerged when you see the penguin outside the water. Now, the light rays that reach you do not travel in a straight line. Rather, they are refracted (bent) toward the vertical as they travel through the air-water surface. That is, if a ray headed toward you is at a moderate angle with the vertical while in the air, it has a smaller angle with the vertical in the water. Your brain cannot take into account that refraction; it still extends the light rays you receive backward along straight lines. As a result, the rays appear to originate higher than they truly do. For example, the rays from the top of the penguin’s head seem to originate higher than they truly do. That means you see a penguin all right, but its height is distorted. If you rise up out of the water and thus eliminate the refraction of the light coming from the penguin, that illusion of distortion disappears.

Here is a cute video about a student who sets out to experience this refraction illusion, not with a penguin but with a common cup, and not in some Antarctic waters but in his bathtub. He shows that sometimes physics is a challenging study, especially when you run out of air. vision from a bathtub of water Scroll down to reach a photo shot from within the water in the swimming pool. But wait. Are these shots real? That is, are the submerged people really submerged? Can you find any clues?

· Walker, J., "What is a fish's view of a fisherman and the fly he has cast on the water?" in "The Amateur Scientist," Scientific American, 250, 138-144 (March 1984)

Want more references? Use the link at the top of this page.

6.86  Transparent when wet
Jearl Walker
November 2014  Here is a story from The Flying Circus of Physics book:

Suppose I demonstrated my mind-reading skill with the following: I’ll have you write a word on a sheet of paper and then place the paper in a standard white envelope where it fits without any need of folding. You seal the envelope. Before you hand me the envelope, you examine it. The word is not visible through the envelope, and the room lacks any bright light that could possibly penetrate the envelope to reveal the word as a shadow.

As I hold the envelope, I’ll have you think of the word so that I can “see” it in my mind. Although I occasionally look at the envelope, I never attempt to hold it up against a light. After a few minutes of concentration, I tell you the word.

The truth is, of course, that I have no mind-reading powers. How do I manage to determine the word? Here’s a hint: Similar physics makes clothing, especially white cotton as in a tee-shirt, semitransparent when wet.

Answer After I receive the envelope, I secretly apply a small amount of grease to it. Normally, light does not penetrate an envelope because it scatters from the fibers and fillers within the paper of the envelope. We can explain the amount of scattering in terms of the index of refraction of a material, which is a measure of how fast light travels in that material. The paper contains pockets of air with a low index and fibers and fillers with a higher index; the large difference in these indexes leads to a large amount of scattering at all the air-pocket surfaces.

I can reduce the amount of scattering by letting the paper absorb grease, which has an intermediate index of refraction. The index does not change very much at an interface between air and grease or an interface between grease and the fibers and fillers. Because the light does not scatter as much, it penetrates the envelope more and can illuminate the ink or pencil marks of the word and the paper on which they lie. The dark marks largely absorb the light, but the surrounding paper scatters some of the penetrating light back through the greasy envelope and finally to me. I can distinguish the marks (and thus the word) by their dark contrast with their surroundings.

Water Wow!

Here is an update to the book’s story: The same kind physics lies behind a certain type of coloring book for children.

Instead of the child adding color to an initially colorless outline of, say, a train engine or a whale, the child adds a small amount of water from a water-filled pen. Here is my granddaughter Olive putting some water on an ocean scene.

A sturdy cardboard lies under the paper, with the same shapes as on the paper.

However, the cardboard figures are colored. When the child adds water to the overlying paper, the paper becomes transparent, making the colors visible.

Later, when the paper dries out, the colors are no longer visible. So, the child can repeat the process. This is a coloring book that can be used indefinitely. Indeed, it can be passed down to the next generation of children in the family.

UV exposure through wet clothing at the beach

One of my FCP stories from 2007 concerned the transmission of UV light through wet clothing worn at a beach. Let’s say the clothing is a white cotton tee shirt. It becomes transparent when wet. So, is there any truth to the common notation that a wet tee shirt offers no protection because of its transmission of light? Research showed that a tee shirt offers protection even if it is wet but not quite as much protection as a dry tee shirt. So, if you want to limit your UV exposure at a beach, wear a tee shirt even if it is wet. To see more on this story, go here and scroll down to item 6.159.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Nassau, K., The Physics and Chemistry of Color: The Fifteen Causes of Color, Wiley, 1983, page 20; 2nd edition, 2001, page 28
· Hecht, E., "Why isn't paper transparent, like glass?" Physics Teacher, 22, 316-317 (1984)
·· Birth, G. S., "Diffuse reflection," Physics Teacher, 24, 138-143 (1986)
··· Bohren, C. F., "Multiple scattering of light and some of its observable consequences," American Journal of Physics, 55, 524-533 (1987)
·· Leskela, M., “A model for the optical properties of paper. Part 1. The theory,” Paper and Timber, 75, Nos. 9-10, 683-688 (1993)
· Bartels, R., and R. Loxsom, “The sun-protection factors of wet and dry T-shirts,” Physics Teacher, 36, 86-89 (February 1998)


6. 89  Criss Angel magic --- walking on water
Jearl Walker
Sep 2008  
Can you walk on water? At one of the links below, you can watch magician Criss Angel walk across a swimming pool filled with spectators. How can he walk on water but you cannot? Let’s start with things that can walk or run on water. As explained in The Flying Circus of Physics book, certain insects and spiders can walk on water and even stand in place. And a certain type of lizard (the basilisk lizard, often called the Jesus lizard) can run across water, but it cannot stand or walk on the water.

The insects and spiders are supported by the surface tension of the water, which is due to the mutual attraction of the water molecules. Because of that attraction, an object of small weight tends to create a dimple in the water surface instead of sinking. In the case of water striders, the insects we commonly see playing on open bodies of water, the support is aided by the nanostructure of the insect legs, which resists water from spreading over the legs.

A basilisk lizard weighs too much to be supported by surface tension. Instead, its support comes from the impact of its feet on the water as it runs.

Each footfall is a slap on the water much like you can slap your hand down onto water. During the impact, the water is not as firm as, say, concrete, but you do feel a sting on your hand. You feel an even greater force, perhaps a damaging force, if you “cannonball” by jumping belly first into water from a large height.

Each footfall by the lizard gives a brief supporting force. As the foot then sinks into the water, it creates a crater. By then the lizard has slammed its other foot down on the water and is beginning to pull its first foot out the crater before the water has time to flood the crater. The repeated brief support with each downward foot slap can be enough to support a juvenile basilisk, but the mature ones are usually too heavy to run over water.

How about Criss Angel walking on water? Surface tension? Foot slap on the water? Here is the video:

Caution: If you don’t want me to spoil this very nice show of magic, stop reading here.

I love magic tricks, partly because I study physics --- magic tricks seemingly defy the laws of physics. Even if you don’t know those laws in some formal or mathematical way, you nevertheless use your lifetime of experience to recognize when the laws are being broken. Criss Angel is quite clearly breaking the laws and doing something physically impossible.

Or is he? Can you guess how he does the trick?

Just below the water surface, from his starting point to his ending point, there is a transparent, solid bridge made of plastic (probably common Plexiglas). The bridge is not thick and has supporting columns at the two ends and probably at several points along its length. You might object to this explanation because at one point we see a woman swim below Angel, to give the impression that nothing solid lies below him. Well, she is simply swimming under the bridge.

You might also object that surely the people in the pool would notice a plastic bridge. Well, I am sure that they did. Everyone in the pool was part of the trick. (I especially love the theatrical pose of one woman who clamps a hand over her mouth in utter “astonishment.” That pose was probably scripted and was about as real as the “reality” we see in “reality television” --- in other words, it is not real.) The part where one person seemingly gets out of Angel’s way was also scripted to give the illusion that the bridge was not there. The person merely stood next to the bridge with one arm elevated over its top and then moved away as Angel approached.

So, why can we not see the bridge? Well, we can see a transparent object submerged in water only if some of the light reaching the object reflects from it to us. However, reflection occurs only if there is a difference in the index of refraction of the object and that of the water. (This index is a measure how light travels in a material.) If there is a close match, then so little light reflects that the submerged object is invisible.

Angel built his bridge out of plastic with a low index of refraction to come as close as possible to the low index of water. To hide the small amount of reflection from the plastic, the cameramen in the pool and alongside it aimed their cameras at low angles so that we could not see clearly into the water. When we do get a penetrating look (with the camera carried by Angel), the view is straight down onto the bridge. In that view, the reflections off the top of the water mask the weaker reflections from the top of the bridge. Still, if I step through that part of the video, I think I see the right-hand edge of the bridge --- there seems to a slight difference in the reflections on the right and left sides of a line that runs vertically up the screen.

Here is a similar magic trick as described in The Flying Circus of Physics book. Place a test tube (or some other transparent glass object) in a large transparent container (such as a large beaker). Fill the container with enough water to cover the test tube. Because the refractive index of the tube is higher than that of the water, the reflections from the test tube surface are bright enough for us to see the test tube.

Now gradually add sugar to the water to increase its index of refraction. The reflections from the test tube gradually dim and thus the visibility of the test tube gradually decreases, until you can no longer see the test tube. (The water, however, does not look any different.)

Bring in your audience and explain that you have the power to mend broken glass with a sweep of your hand. As your audience watches, wrap paper towels around another test tube and then carefully break it down to a powder by striking the towels with a small hammer. Carefully pour the powder into the beaker, explaining that the beaker is filled with water. You can even scoop up a bit of the water to convince the audience. (Take great care not get any powder on your fingers and then onto your face.) Neither the powder nor the hidden test tube will be visible to the audience but the invisibility of the powder will not be surprising because dust is hard to see anyway.

Sweep your hand slowly over the beaker as you chant, “I command that the interatomic forces mend this tube!” Reach into the water and then pull out the hidden test tube. The audience will then surely realize that you are indeed the master of interatomic forces. (Reassure them that you will use the power wisely and not to take over the world.)

I like the Criss Angel magic a lot because, unlike a traditional magician, his style is very disarming. (He pretends to be unsure of a trick that he surely has repeatedly rehearsed, and he speaks with plenty of broken, seemingly spontaneous sentences, as if he is just then working out what to say. He is very convincing.) Next month I’ll examine his trick in which he floats between two buildings, about two stories above a parking lot. I started this story here with the question, “Can you walk on water.” Well, next month I’ll start with, “Can you float between two buildings?”

This story idea was suggested by teacher JoAnn Hoty and her class at West Lake High School in West Lake, Ohio. 

· Connolly, W. C., and T. L. Rokoske, "The disappearing dropper," Physics Teacher, 18, 467 (1980)
· Ellenstein, M., "Magic and physics," Physics Teacher, 20, 104-106 (1982)

For references about water striders and basilisk lizards, go to
and then scroll downward to items 2.42 (basilisk lizards) and 2.80 (water striders)

6.90  Transparent frogs
Jearl Walker
Feb 2008

The photo here (courtesy of Virginia L.Shuford Freire) shows a “glass frog” that is so transparent that you can clearly see the internal organs. Why aren’t you and I transparent? Transparency would have its advantages. For example, if something went wrong with an internal organ, a doctor could look directly at the organ without having to slice open the body. (I am definitely in favor of not being sliced open. However, I don’t think I want my digestive system to be on full display when I go the beach. So, maybe being nontransparent is best.)

Your skin is not transparent for the obvious reason that light does not pass through it as it would pass through common picture frame glass that we use to mount a photograph on a wall. The difference is that in skin the light undergoes both absorption (which removes the light) and scattering (which redirects the light in a scrambled fashion). Clear glass has little absorption and little scattering. Thus, light can pass through the glass, reflect from the photograph, and then pass through the glass again without being scrambled. If you intercept the light, you can recognize what is in the photograph.

Skin is different. Part of the light is absorbed by melanin, the polymer that gives pigmentation to the skin. The rest of the light might penetrate the skin, but it scattered so much by the skin components, primarily collagen, that it becomes diffused (spread out and scrambled). Some of the light might actually reach an internal organ. Indeed, some of the researchers listed below point out a common observation about the penetration of light: If you hold a finger in front of a flashlight (torch) in an otherwise dark room, you can see light that passes through the finger. It is red because the red end of the visible spectrum is transmitted through skin, fat, and muscle better than the blue end. However, the transmitted light is too scrambled for you to see an outline of the finger bone as you would in an x ray image of your finger.

The same researchers also point out that if you stand in bright sunshine, your brain is actually illuminated by light that passes through the forehead. The level of illumination is low, but if you had the same amount on a printed page, you would be able to read the page easily enough. Thus, if you shine bright light on your body, some of the light can reach your internal organs.

When that light reflects from an organ and then travels back through the skin, it becomes scrambled by the repeated scattering. So, the emerging light is both very weak and very scrambled, and we cannot see an image of the internal organ.

The scattering involves a property called the index of refraction, which is a measure of the effective speed of light in a material. Greater index means a slower effective speed. However, here we are not concerned with how fast light travels in the skin. Rather, we are concerned with the points where the index sharply changes value ---- light scatters at such a point. When light passes through skin, much of the scattering occurs where the water in the skin (lower index of refraction) lies against collagen (higher index of refraction).

This scattering can be decreased by applying certain substances, such as glycerol, in a process called optical clearing. The index of refraction of such an agent nearly matches the index of refraction of the collagen. So, when the agent soaks into the skin, replacing the water, the amount of scattering is decreased, and thus the amount of scrambling is also decreased. Now the light emerging from the skin might be able to produce an image of the interior, such as the blood network. If you put glycerol on your arm, you don’t noticeably become transparent like a glass frog (gosh, that would be cool, wouldn’t it?), but the light emerging from the skin might be processed to provide an image of the interior.

Long ago, researchers discovered that they could increase the skin transparency of certain frogs by feeding them special compounds, which I presume reached the skin and acted as optical clearing agents. Recently a researcher reported how he used genetic manipulation to produce a transparent frog. (Surely this story will provide a new cartoon series--- “The Teenage Mutant Transparent Frogs.” Not only do they know martial arts, but only their digestive systems are visible, which scares their opponents into running away.)

The champions of transparent skin are still the glass frogs of the tropics. Not only does the light undergo fairly little scattering in the skin because the index of refraction of the skin is nearly uniform, but a second effect comes into play, an effect that is sometimes known as shower curtain optics.

As I explain in The Flying Circus of Physics, the glass or plastic doors on many shower stalls are textured to provide more privacy to a modest bather. The texture is intended to scramble the light passing through it so that an observer outside the stall can see only a blurry image of the bather through the door. However, if the bather stands immediately next to the door, the image is quite clear and modesty is totally lost.

Let’s concentrate on a single spot on the bather, who initially stands near the door. The light you receive from the spot illuminates only a small region on the textured surface. Although the light is scattered by the textured surface, the smallness of the illuminated region allows you to form a fairly sharp image of the spot. The composite of such individual spots provides a clear image of the bather.

Now let the bather back away from the door. The light you now receive comes through a larger region on the textured door and you can form only a larger image of the spot. The images of adjacent spots now overlap, which means that their composite is only a blurry image of the bather.

In a glass frog, the light reaching you from an internal organ is scattered in the skin like light is scattered in a textured shower door, but the organs are so close to the skin that you form a fairly clear image of them. Physics is everywhere, and here it connects tropical frogs with modest bathers. news report almost the same report

Miller, D., and G. Benedek, Intraocular Light Scattering: Theory and Clinical Application, Charles C. Thomas, 1973, pages 68-72
· · Anderson, R. R., and J. A. Parrish, “The optics of human skin,” Journal of Investigative Dermatology, 20, No. 15, 13-19 (1981)
· Leroy, D., A. Dompmartin, and P. Deschamps, “Increased penetration of epidermis by high intensity ultraviolet rays following the application of Vaseline oil,” Photodermatology, 3, 51-52 (1986)
· Walker, J., "When a polymer sheet is stretched, it may 'neck' long before it snaps" in "The Amateur Scientist," Scientific American, 262, 100-105 (February 1990)
· Benaron, D. A., W. F. Cheong, and D. K. Stevenson, “Tissue optics,” Science, 276, No. 5321, 2002-2003 (27 June 1997)

· · · Dror, I., A. Sandrov, and N. S. Kopeika, “Experimental investigation of the influence of the relative position of the scattering layer on image quality: the shower curtain effect,” Applied Optics, 37, No. 27, 6495-6499 (20 September 1998)
· Choi, B., L. Tsu, E. Chen, T. S. Ishak, S. M. Iskandar, S. Chess, and J. S. Nelson, “Determination of chemical agent optical clearing potential using in vitro human skin,” Lasers in Surgery and Medicine, 36, 72-75 (2005)
· Bashkatov, A. N., E. A. Genina, A. A. Gavrilova, A. B. Pravdin, D. Tabatadze, J. Childs, I. Yaroslavsky, G. Altshuler, and V. V. Tuchin, “What exactly causes increase in skin transparency: water replacement or dehydration?” Lasers in Surgery and Medicine, Supplement 18, p. 84, abstract # 284 (2006)
· Hirshburg, J., B. Choi, J. S. Nelson, and A. T. Yeh, “Collagen solubility correlates with skin optical clearing,” Journal of Biomedical Optics, 11, No. 4, article # 040501 (3 pages) (July/August 2006)
· · Hirshburg, J., B. Choi, J. S. Nelson, and A. T. Yeh, “Correlation between collagen solubility and skin optical clearing using sugars,” Lasers in Surgery and Medicine, 39, 140-144 (2007)
· · Proskurin, S. G., and I. V. Meglinski, “Optical coherence tomorgraphy imaging depth enhancement by superficial skin optical clearing,” Laser Physics Letters, 4, No. 11, 824-826 (2007)
· “See-through frog offers inside information,” Nature, 449, 521 (4 October 2007)
· Castroviego-Fisher, S., I. De la Riva, and C. Vila, “Transparent frogs show potential of natural world,” Nature, 449, 972 (25 October 2007)
· Erren, T. C., R. J. Reiter, V. B. Meyer-Rochow, “Frog transparency led to discovery of melatonin,” Nature, 451, 127 (10 January 2008)

Want more references? Use the link at the top of this page.

6.95  Opal coloration in a beetle
Jearl Walker
July 2006   As discussed in the book, the colors of an opal are due to the diffraction of light by an ordered stacking of tiny spheres: White light enters an opal but the stacking arrangement scatters back only light in a narrow color (or wavelength) range. The rest of the entering light undergoes destructive interference (the waves cancel one another) after scattering from the arrangement.
     Similar diffraction of light occurs in the scales on the Australian beetle Pachyrhynchus argus. A scale contains an inner structure of tiny transparent spheres in an ordered packing, an arrangement known as a photonic crystal. If white light shines on the beetle, the light reflected (scattered) by the scales has a metallic color of yellow-green. The spacing of the sphere arrangement determines the color of the reflected light but the beetle is not iridescent like many types of butterflies because the spacing varies across the scales, giving an overall yellow-green appearance.

· Parker, A. R., V. L. Welch, D. Driver, and N. Martini, “Opal analogue discovered in a weevil,” Nature, 426, 786-787 (18/25 December 2003)

Want more references? Use the link at the top of this page.


6.97  Star sapphire illusion
Jearl Walker
June 2015  When you look down on a star sapphire that is illuminated by a small light source, why do you see a six-point star floating above the stone?

The star is produced by light scattering from needles of titanium oxide grouped into one of three orientations that are separated by 120°.

The light scattered by each group forms a line in your view. So, you see three lines that intersect at their midpoints and form the six rays of a star. If the gem is cut with a round or oval dome (instead of being cut with facets), the star appears to lie somewhat above the dome, giving the floating appearance. The image is virtual, meaning that it is something your visual system conjures up to make sense of the light. A luminous star would not appear on a card placed at the star’s apparent position.

More links: use one of their group photos

Dots · through ··· indicate level of difficulty
Book reference style: author, title, publisher, date, pages
· Nassau, K., The Physics and Chemistry of Color: The Fifteen Causes of Color, second edition, Wiley, 2001, pages 240-241


6.100  Seeing a shock front on an airplane wing
Jearl Walker

April 2010    I was in a large commercial airliner at its cruising altitude, bored out of my mind, searching the sky for any curious optical effects, as I always do when sitting next to a window. No luck. Not a single bright spot or colored band appeared. Then suddenly I noticed an odd line extending along the wing. At first I dismissed the line as simply being an edge of metal section on the wing and could not figure out why I even noticed it. Then it shimmied slightly when slight air turbulence oscillated the wing. Metal edges do not shimmy.

Still, what I saw was just a shadow, probably some freak alignment of the sun with a structure on top of the cabin. But I immediately knew that was wrong because the sun was fairly high above my side of the airplane --- thus, nothing could cast a shadow along the brightly lit wing.

Then the pilot abruptly banked the airplane, bringing the wing up and turning the airplane so that the sun was about 25 degrees above the wingtip. The shadowy line suddenly transformed into distinct bright and dark bands.

When the pilot leveled out the wing, increasing the angle between the wingtip and the sun in my view, the bands became less visible. After about half an hour, they disappeared.

When I was seeing was an optical effect due to the sunlight refracting through a shock front just above the wing. The airplane was subsonic (flying slower than the speed of sound at our altitude), but the air was apparently supersonic as it was forced to flow up and then over the wing. Somewhere over the wing, its speed dramatically decreased and its density dramatically increased. That abrupt transition is called a shock front.

When light rays passes through an interface between materials of different density, they bend into new directions. If the air above the wing had been uniform in density, the rays of light from the sun would have evenly illuminated the top of the wing. However, with a shock front separating dramatically different densities of air, any ray passing through the shock front was bent into a new direction. That bending concentrated some of the rays to form the bright band I saw, directing them away from the dark band I saw.

In spite of my numerous air trips, I saw evidence of a shock front only once more. However, the optical effect was different: a dark band stood upright about halfway out on the wing, noticeably distorting the details of the wing’s outer half. As with other bands, it caught my attention only because it shimmied. It moved it much more as I move from window to window along the fuselage (there were lots of empty seats).


The dark band was due to light rays skimming through a shock front, but they originated from details of the sunlit wing. When the rays from adjacent details on the wing passed through the shock front, they were bent by different amounts. The resulting spread in the rays left the region between the details relatively dark in my view, and the composite of these dark spots formed the dark band.

Here are some links to videos of the shock-front bands. In each, the bands are difficult to see (far more difficult than from an airplane window). Look for distortions of the wing that move slightly.

If you would like more ideas about things to look for while flying, print out this month’s “article of the month” (it is another one of the options here in the “news/updates”). It comes from my column in Scientific American for September 1988. Next month I shall post the sequel, in which I describe even more things to look for on a long, otherwise tedious flight.


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Lamplough, F. E., "Shock-wave shadow photography in tunnel and in flight," Aircraft Engineering, 23, 94-103 (April 1951)
· Wood, E. A., Science from Your Airplane Window, Dover, 1975, pages 71-72
· Van Dyke, M., An Album of Fluid Motion, Parabolic Press, 1982, pages 132-133
· Hewish, A., "In-flight movies," Nature, 306, 118 (1983)
· Walker, J., "Shock front phenomena and other oddities to entertain a bored airline passenger" in "The Amateur Scientist," Scientific American, 259, 132-135 (September 1988)

6.103  Solar images beneath a tree
Jearl Walker
September 2013    During a solar eclipse, what produces the many small images of the Sun in the shadow cast by a tree? Are solar images in the tree’s shadow at other times? Why do shadow images of leaves, sometimes with a pair of edges, one inside the other, appear beneath a tall canopy of leaves? Why don’t they appear beneath shorter trees?

The eclipse images are produced by small holes in the leaves or between adjacent leaves. Each hole functions like a pinhole camera, throwing an image of the Sun into the tree’s shadow on the ground. The images are produced even when there is no eclipse, but they may be more difficult to distinguish because the overall glare of sunlight from the sky and the landscape partially illuminates the shadow. During an eclipse, that glare is diminished by the overall darkening and the images are then more perceptible. In either situation, the images are much easier to see on a flat surface than on uneven or grassy ground.

A leaf shadow seen beneath a tall canopy of leaves is cast by a low-lying leaf that is illuminated by sunlight streaming through a hole higher in the canopy. If a low-lying leaf is illuminated by two higher holes, you might see two overlapping shadow images, with one leaf-edge image inside a second leaf-edge image.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Bragg, W., The Universe of Light, Dover, 1959, pages 29-31
· Arakawa, H., "Crescent-shaped shadows during a partial eclipse of the Sun," Weather, 16, 254-255 (1961)
· Wood, E., Science for the Airplane Passenger, Houghton Mifflin Co., 1968, pages 66-67
·· Miller, E. E., and J. M. Norman, "A sunfleck theory for plant canopies II. Penumbra effect: intensity distributions along sunfleck segments," Agronomy Journal, 63, 739-743 (1971)
· Corliss, W. R., Rare Halos, Mirages, Anomalous Rainbows and Related Electromagnetic Phenomena, Sourcebook Project, 1984 (PO Box 107, Glen Arm, MD 21057), pages 201-202
· Anderson, M. C., and E. E. Miller, "Forest cover as a solar camera: penumbral effects in plant canopies," Pinhole Journal, 1, No. 1, 3-6 (December 1985)
· Falk, D. S., D. R. Brill, and D. G. Stork, Seeing the Light. Optics in Nature, Photography, Color, Vision, and Holography, Harper & Row, 1986, pages 33-34
· March, R. H., "Car in a driveway," Physics Teacher, 27, 662 (1989)
·· Handojo, A., "Solar eclipse observation: some simple devices," Journal of the Optical Society of America, 28, 4293-4297 (1989)
· Romer, R. H., "Spots on the lawn," Physics Teacher, 28, 326 (1990)
· Greenslade Jr., T. B., “Pinhole images of the eclipsing sun,” Physics Teacher, 32, No. 6, 347 (September 1994)
· Lynch, D. K., and W. Livingston, Color and Light in Nature, 2nd edition, Cambridge University Press, 2001, pages 201-203
·· Sigismondi, C., “Measuring the angular solar diameter using two pinholes,” American Journal of Physics, 70, No. 11, 1157-1159 (November 2002)


6.106  Windshield light streaks
Jearl Walker
March 2013  Here is a photograph of the low Sun as seen through the windshield of my car. It shows a bright curved streak extending along the glass from my direct view of the Sun.

The streak is due to the scattering of light from the grooves that my windshield wiper has curved in the grimy material coating the outside surface of the glass. The material might be road debris or, during snow falls, thin layers of salt from the salt used on the roads to clear snow and ice.

Because the windshield wiper rotates around a pivot point, the grooves tend to be circular and the light streak tends to be radial to the pivot. However, the glass is curved, which distorts the circular grooves and curves the light streak.

The streak is narrower near the pivot point because the circular grooves in the glass grim are more strongly curved there. When a car approaches me at night, I see a light streak above and below each headlamp of the car.

Because my eyes are separated, each sees its own light streak. Sometimes I mentally combine the two streaks. Then they appear to form a single streak that extends outward from my windshield, as if there is a well-lit path extending outward.

In addition to the main streak, dimmer streaks extend away from my direct view of the Sun because light becomes momentarily trapped within the glass, reflecting or scattering from the two sides of the glass. A bit of the light escapes toward me at each reflection point on the interior surface.


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Kirkpatrick, P., "A binocular illusion," American Journal of Physics, 22, 493 (1954)
· Walker, J., "What do phonograph records have in common with windshield wipers?" in "The Amateur Scientist," Scientific American, 261, 106-109 (July 1989)

6.113 Pub trick --- ouzo effect
Jearl Walker
August 2014   Certain aniseed-based alcoholic drinks, such as ouzo in Greece, le pastis in France, raki in Turkey, and sambuca in Italy, display a peculiar behavior: At one point as water is gradually added to the fairly clear drink, the drink suddenly turns milky white. What causes this change? That is, what does the water do, and what accounts for the change in the drink’s appearance? The effect can be reversed if more alcohol is added.

Water added to Ouzo

Ouzo added to water

Each of these drinks is a solution with a uniform distribution of aniseed oil and ethanol alcohol. When a light beam (such as sunlight) is sent into the solution, it emerges on the opposite side as a beam. When water (a third liquid) is added, things can change because the aniseed oil cannot dissolve in water. Initially the drink is transparent (a light beam still travels through it as a beam). However, when the water content reaches a certain fraction of the liquid, said to be a critical value, the oil molecules spontaneously form drops that are suspended in the liquid. The drink is said to undergo a phase transition, switching from a homogeneous (uniform) liquid–liquid solution to a nonhomogeneous ­liquid–droplet dispersion (or emulsion). The drops scatter visible light. So any beam sent into the drink is scattered into many directions, which gives the drink a milky appearance. If more of the alcohol is poured into the drink, dropping the water content below the critical value, the phase transition is reversed and the drink becomes clear again.


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
·· Mayorga, A., and D. Thompson, “A critical exponent of an aniseed-based liquor,” American Journal of Physics, 64, No. 5, 621-623 (May 1996)
· Vitale, S. A., and J. L. Katz, “Liquid droplet dispersions formed by homogeneous liquid-liquid nucleation: ‘the ouzo effect’,” Langmuir, 19, 4105-4110 (2003)
· Grillo, I., “Small-angle neutron scattering study of a world-wide known emulsion: Le Pastis,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, 225, Nos. 1-3, 153-160 (2003)
·· Sitnikova, N. L., R. Sprik, G. Wegdam, and E. Eiser, “Spotaneously formed trans-anethol/water/alcohol emulsions: Mechanism of formation and stability,” Langmuir, 21, 7083-7089 (2005)
·· Scholten, E., E. van der Linden, and H. This, “The life of an anise-flavored alcoholic beverage: Does its stability cloud or confirm theory?” Langmuir, 24, 1701-1706 (2008)

6.117  Butterflies in daylight, moths in nightlight
Jearl Walker
September 2007
Whenever light reaches a surface (or interface) where the index of refraction changes, part of the light reflects. That index is a measure of the effective speed of the light as it interacts with the atoms along its path. The index is low (and the effective speed is high) for air. The index is higher (and the effective speed is lower) for most transparent materials such as water, glass, and your cornea. When light reaches your eye, a small part (only a few percent of the intensity) reflects from the surface of the cornea where the light encounters an abrupt change in the index of refraction. Thus, some of the light does not enter the eye to travel to your retina. The loss is negligible and unnoticed because you nearly always move around in well-lit places, whether in daylight or artificial light. So, why would you care about a slight loss of light?

Butterflies are like you---they move around in the day in well-lit places. The eye of a butterfly is very different from your eye, however, because it is a compound eye like the eyes on all insects. That is, it consists of a great many separate sections (ommatidia) along which the light is channeled to reach light-sensitive molecules where the light is detected. Still, the butterfly eye is like your eye in that part of the light is reflected at the outer surface where the light encounters an abrupt change in the index of refraction. However, as with you, the loss is unimportant because of the abundant light during the day.

Moths are different---they move around in dim light at night. Although a moth eye is a compound eye like a butterfly eye, the surface is not the same. Instead of a smooth surface as on a butterfly eye, the moth eye is covered with microscopic, closely spaced bumps with the technical name corneal nipples. The index of refraction within a bump is moderate, just as in a butterfly eye. However, the arrangement of bumps provides a smooth transition from the index of air to the index of the interior of the eye. As a light wave reaches an ommatidium, it first encounters the narrow tops of the bumps and so the index of refraction is dominated by the air between the tops. That means that there is not much change in the index. As the light continues toward the eye, it encounters progressively wider portions of the bumps and thus less air, and so the index progressively increases until it is solely due to the eye at the base of the bumps.

This arrangement of corneal nipples to eliminate reflection seems to be an advantage to moths, so that they can see better at night. However, the increase in light intensity sent into the eye is only a few percent. If 96% of the light would have gone into the eye without the corneal nipples, would the increase to 100% of the light make any substantial difference?

Here is a better argument from the current research: A moth eye has corneal nipples not so that the moth can see better at night but so that the moth has no eye glare in daylight when predators search for the moth to eat it. If the reflection off the eyes sends out more light than the rest of the moth, it would act like a beacon to a predator that effectively said, “Good food here. Come on down.” So, corneal nipples and their effect on the index of refraction allow moths to sleep relatively safely during daylight instead of becoming a predator’s lunch.

Some types of modern glass and plastic covers have a porous surface that mimics the surface of a moth’s eye. These antireflective surfaces are useful when the reflections are distracting (as when a surface might reflect direct sunlight) or when the transmission of light through the surface must be maximized (as in a solar panel). Moth eye optics is yet another example of where industry benefits from an existing natural design. Summary of research paper 

· ·
Stavenga, D. G., S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proceedings of the Royal Society B, 273, 661-667 (2006)
· Lau, T. F. (Stanley), E. M. Gross, and V. B. Meyer-Rochow, “Sexual dimorphism and light/dark adaptation in the compound eye of male and female Acentria ephemerella (Lepidoptera: Pyraloidea: Crambidae),” European Journal of Entomology, 104, 459-470 (2007)

Want more references? Use the link at the top of this page.

6.119 Color-shifting paint and ink of cars and currency

Jearl Walker

May 2010   Most cars have a particular color, one that does not depend on your perspective. However, some cars, such as the one shown here, have color-shifting paint so that as the car moves across your view or turns, the colors change.

Although some people may think that such color changing is gaudy, I must confess that I was mesmerized when I recently saw a color-shifting car turn in front of me. Here is a video that shows how the colors change as the video camera is moved around a stationary car:

Color shifting inks have been used on the currency of the United States and other countries for years. The problem is that governments worldwide must scurry to stay ahead of counterfeiters who are quick to use the latest technology to duplicate paper currencies. Some of the security measures used to thwart counterfeiters are security threads and special watermarks (both of which can be seen if the currency is held up to the light) and microprinting (which consists of dots too small to be reproduced by a scanner).

However, one feature that is most difficult for a counterfeiter to duplicate is the variable tint that results from color-shifting inks. For example, the number in the lower right corner of the front face of U.S. paper currency ($10 or larger) contains color-shifting ink.

If you look directly down on the number, it is red or red-yellow. If you then tilt the bill and look at it obliquely, the color shifts to green. A copy machine can duplicate color from only one perspective and therefore cannot duplicate this shift in color. Here is a video that displays the color-shifting and other security measures used on the newly designed $100 bill that was recently introduced in the United States:

The color-shifting inks and paints depend on the interference caused by thin transparent flakes suspended in regular ink. One scheme is shown in the figures here.

Part a shows light passing through the regular ink above the flakes and down to the flakes. Part b is a detail of one of the flakes and shows the thin layers of chromium (Cr), magnesium fluoride (MgF2), and aluminum (Al) through which the light travels. The Cr layers function as weak mirrors, the Al layer functions as a better mirror, and the MgF2 layers function like soap films. The result is that light reflected upward from each boundary between layers passes back through the regular ink and then undergoes interference at an observer’s eye.

The light waves of a certain color in the visible range undergo constructive interference, reinforce one another, and are thus seen by the observer. The light waves of the other colors in the visible range undergo destructive interference, cancel one another, and are thus not see by the observer. White light illuminates the ink and its flakes, but only a certain color is seen by the observer.

Which color undergoes constructive interference depends on the thickness L of the MgF2 layers. In U.S. currency printed with color-shifting inks, the value of L is designed to give fully constructive interference for red or red-yellow light when the observer looks directly down on the currency. When the observer tilts the currency and thus each flake, the light reaching the observer from the flakes undergoes constructive interference for green light. The shift to this other wavelength is due to the longer path taken by the light through tilted flakes (it does not simply travel down through distance L and then back up through it, but instead takes a slanted path down and then a slanted path back up). Thus, by changing the viewing angle, the observer can shift the color that is strongly sent back up out of the ink.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Dobrowolski, J. A., K. M. Baird, P. D. Carman, and A. Waldorf, “Optical interference coatings for inhibiting of counterfeiting,” Optica Acta, 20, No. 12, 925-937 (1973)
· Dobrowolski, J. A., F. C. Ho, and A. Waldorf, “Research on thin film anticounterfeiting coatings at the National Research Council of Canada,” Applied Optics, 28, No. 4, 2702-2717 (15 July 1989)
· Hobbs, J. R., “Banknotes to get optical counterfeit deterrents,” Laser Focus World, 30, No. 4, 32-33 (April 1994)
· Schafrik, R. E., and S. E. Church, “Protecting the greenback,” Scientific American, 273, No. 1, 40-46 (July 1995)
· Zurer, P., “High-tech ink to be added to U.S. bills,” Chemical & Engineering News, 73, No. 41, 7-8 (9 October 1995)
· Lipkin, R., “New greenbacks. How to make a buck---literally,” Science News, 149, 58-59 (27 January 1996)
· Phillips, R. W., and A. F. Bleikolm, “Optical coatings for document security,” Applied Optics, 35, No. 28, 5529-5534 (1 October 1996)
· Murphy, J. C., D. C. Dubbel, and R. C. Benson, “The Securities Technology Institute for counterfeit deterrence,” Johns Hopkins APL Technical Digest, 18, No. 2, 295-301 (April-June 1997)
·· Pfaff, G., and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chemical Reviews, 99, 1963-1981 (1999)
· Burns, D. A., “Detection of counterfeit currency and turquoise,” in Practical Spectroscopy, Vol. 27, 2001, pages 783-801
· Anderson, L., photo, in “After Image,” Optics & Photonics News,

6.126  Glass buildings act as polarization insect traps
Jearl Walker
Aug 2008  
Here is a good example of the difference between a scientist and a normal person. In April and May of every year, countless caddis flies (H. pellucidula) emerge from the river banks of the Danube in Budapest and swarm onto the glass windows of the high-rise buildings, where they mate (minutes) and then rest (hours).
Upon seeing the many thousands of the flies on the glass windows, a normal person would just say, “What a mess. Those flies are stupid.” However, a scientist seeing the swarms of flies would say, “That’s very strange. Why are the flies driven to glass windows? Why mate on glass?”

Gyorgy Kriska, Peter Malik, Ildiko Szivak, and Gabor Horvath of Eotvos University in Budapest are such curious scientists. (The photos here are from their recent paper, "Glass buildings on river banks as 'polarized light traps' for mass-swarming polarotactic caddis flies," Naturwissenschaften, 95, pages 461-467 (2008).) For years, Horvath and other researchers have realized that some aquatic insects can detect the presence of ponds and other bodies of water by the sunlight reflected by the water. If the water is calm, the reflection can be mirror-like and thus bright, but the clue that the caddis flies use is the polarization of that reflected sunlight.

Any ray of light consists of oscillating electric fields. Such a field has a size and a direction, and the direction must always be perpendicular to the ray itself. However, for any common ray of light, such as from a light bulb, there is no preferred direction of the fields --- they have any possible direction in a plane perpendicular to the ray. Such light is said to be unpolarized.

However, in some circumstances, all the field directions are eliminated except along a single axis perpendicular to the ray. You have encountered such polarized light in sun glare, especially on blacktop roads and bodies of water. The glare, due to the reflection of sunlight from those surfaces to your eyes, can be harsh, perhaps resulting in eyestrain and headaches. To decrease the glare, you can wear common sunglasses which absorb light, thus dimming the glare and also the light from everything else in your view. However, people who work in such glare know a better solution --- they wear polarizing sunglasses because those sunglasses eliminate primarily the glare without overly reducing the light from everything else.

Suppose you fish for a living. When you look toward a fairly low sun, you intercept sunlight that reflects from the water. The sunlight that illuminates the water is unpolarized, but the reflected light (that is, the glare) is polarized with horizontal electric fields. Polarizing sunglasses contain polarizing filters that are oriented so as to absorb light with that type of polarization. Thus, they absorb the glare while not absorbing as much of the rest of the light.

The eyes in some types of aquatic insects, such as caddis flies, are sensitive to the polarization of light and can detect when light is horizontally polarized. When one of these insects intercepts light reflected from a body of water, the polarization of the light signals the insect about the presence of the water. This is important to the flies, because they mate and then deposit the eggs on water.

Thus, horizontally polarized light is really appealing to the flies. The hitch is that light reflected from blacktop roads and certain other horizontal surfaces also becomes horizontally polarized and thus is very appealing to the flies. Mating on a blacktop road is, of course, not a good idea.

So, what about the glass windows near the Danube? They are certainly not horizontal like water or a blacktop road. However, the ones that face the sun during sunset produce horizontally polarized light. As the insects swarm from the Danube, sensing the light, the urge to mate drives them to the source of the light, the glass windows. As they arrive, they do indeed find opportunities for mating, just as if they are in open water, never mind the surface is vertical instead of horizontal. As the researchers point out, the flies might then be mentally trapped there, not understanding that there is no water until they die from dehydration. And any eggs laid there will, of course, not survive. Still, the blinding urge to mate at the source of the blinding polarized light lures them into what the researchers describe as “polarized light traps.”

The mantra of FCP, both the book and this web site, is that physics is everywhere, even in the springtime swarming of caddis flies on windows near the Danube.

·  Kriska, G., P. Malik, I. Szivak, and G. Horvath, “Glass buildings on river banks as ‘polarized light traps’ for mass-swarming polarotactic caddis flies,” Naturwissenschaften, 95, 461-467 (2008)

6.128  Desert ant navigation
Jearl Walker
November 2006 
   In the Flying Circus of Physics book, I describe how the desert ant Catglyphis fortis can find its way back to its nest after traveling a long complicated path away from the nest to search for food. In spite of the hundreds of course changes, when it is ready to return, the ant simply turns toward the nest and moves along a straight line until it reaches the nest. The ant knows the way home because during the outward trip it continuously performs vector addition of all its displacements, both the length and direction of the displacements. So, the way home from any spot is the reversal of the net vector from the nest to that point.
    This is astonishing, especially to my students who struggle to add only two or three vectors (using a calculator). Here, this tiny ant with a tiny brain (and no calculator) can add hundreds of vectors (and with no guidance from a physics instructor)!
    Recent research shows that the ant's ability to find the direct route home works even when the terrain is hilly, such with sand dunes. Apparently, the ant can project its motion onto a horizontal plane. So, if it follows a complicated outward route involving a lot of up and down travel, it knows the direct route home even if that direct route involves lots of up and down travel over other portions of the hills. That is, it can find the horizontal components of all the individual displacements and then sum those components. Somehow, this mathematical ability must be genetically coded in the ants. Too bad mathematics is not coded in your genes---math classes would have been a lot easier.

· Wehner, R., and M. Muller, “The significance of direct sunlight and polarized skylight in the ant’s celestial system of navigation,” Proceedings of the National Academy of Sciences of the United States of America, 103, No. 33, 12575-12579 (15 August 2006)
· Ronacher, B., E. Westwig, and R. Wehner, “Integrating two-dimensional paths: do desert ants process distance information in the absence of celestial compass cues? Journal of Experimental Biology, 209, 3301-3308 (2006)
·  Muller, M., and R. Wehner, “Wind and sky as compass cues in desert ant navigation,” Naturwissenschaften, 94, 589-594 (2007)
· “Pedometer helps ants get home,” Journal of Experimental Biology, 210, i (2007)
· Wittlinger, M., R. Wehner, and H. Wolf, “The desert ant odometer: a stride integrator that accounts for stride length and walking speed,” Journal of Experimental Biology, 210, 198-207 (2007)
· Narendra, A., “Homing strategies of the Australian desert ant Melophorus bagoti. I. Proportional path-integration takes the ant half-way home,” Journal of Experimental Biology, 210, 1798-1803 (2007)

Want more references? Use the link at the top of this page.

6.151 Pattern formed in the shadow of a solid ball or circular disk
Jearl Walker
September 2010   In 1818, Augustin Jean Fresnel submitted a wave model of light to a competition at the French Academy. Simeon D. Poisson, one of the members of the judging committee, argued strongly against the model, attempting to reduce it to absurdity with this thought experiment: If an opaque object with a circular cross section (such as a coin or a ball) is illuminated with a beam of light, Fresnel’s wave model predicted that a bright spot should appear at the center of the shadow cast by the object on a distant viewing screen.

Dominique F. Arago, another committee member, arranged to test the prediction in spite of the absurd conclusion. Surprisingly, he found the bright central spot. Through a quirk of history, the spot is now known as either the Poisson spot or the Arago spot, although neither man initially believed in its existence.

Here is my photograph of the pattern produced by a small opaque disk that was illuminated by the red light of a helium neon laser. The pattern appeared on a sheet of paper, which I photographed at a small angle to the laser beam.

To understand the formation of the spot, first suppose that the source of light is a distant, bright point and that the imaging is done with a solid ball. When the light waves reach the ball, they diffract around its sides, spreading not only radially outward but also into the shadow region of the ball. If a screen is placed well behind the ball, the light forms a small diffraction pattern of bright and dark concentric circles on it. The center of the pattern is a bright point because waves passing on the opposite sides the ball travel the same distance to reach the center.
The waves start out in phase (in step) at the edge of the ball because they are part of the same wave coming from the laser. Because they travel equal distances to reach the center point, they must still in phase when they arrive. Thus, they reinforce each other at the center and undergo constructive interference, giving a bright spot.

The first dark circle surrounding the center is due to destructive interference in which waves arrive out of step and thus cancel each other. Consider the top of the dark circle. Waves passing the bottom of the ball must travel a longer distance to reach that point than waves passing the top of the ball. The extra distance amounts to half a wavelength. Again the waves from top and bottom start out in phase at the edge of the ball. However, because of the difference in the lengths of the path, they arrive at the top of the circle out of step.


The rest of the pattern is due to similar constructive or destructive interference. In some places, waves from opposite sides of the ball differ in the travel distance by an integer number of wavelengths, which results in constructive interference because that puts the waves in phase. In other places the difference in the travel distance amounts to an odd number of half wavelengths, which results in destructive interference because that puts the waves out of phase.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Hufford, M. E., "The diffraction ring pattern in the shadow of a circular Object," Physical Review, Series 2, 7, 545-550 (1916)
·· Sommerfeld, A., Optics, Academic Press, 1954, page 216
·· Jenkins, F. A., and H. E. White, Fundamentals of Optics, McGraw-Hill, 1957, pages 359-360
· Pohl, R. W., Optik und Atomphysik, 12th edition, Springer, 1967, pages 92-93
· Rayleigh, Lord, "Shadows" in The Royal Institution Library of Science: Physical Sciences, W. L. Bragg and G. Porter, editors, Elsevier, 1970, vol. 5, pages 54-61
·· Meyer-Arendt, J. R., Introduction to Classical and Modern Optics, Prentice-Hall, 1972, page 200
··· Rinard, P. M., "Large-scale diffraction patterns from circular objects," American Journal of Physics, 44, 70-76 (1976)
· Johnston, J. B., "Projecting Poisson's spot," Physics Teacher, 16, 179 (1978)
·· Hecht, E., and A. Zajac, Optics, Addison-Wesley, 1979, pages 373-375
··· Harvey, J. E., and J. L. Forgham, "The spot of Arago: new relevance for an old phenomenon," American Journal of Physics, 52, 243-247 (1984)
· Walker, J., "A ball bearing aids in the study of light and also serves as a lens" in "The Amateur Scientist," Scientific American, 251, 186-193 (November 1984)
··· English Jr., R. E., and N. George, "Diffraction patterns in the shadows of disks and obstacles," Applied Optics, 27, 1581-1587 (1988)
··· Hovenac, E. A., “Fresnel diffraction by spherical obstacles,” American Journal of Physics, 57, No. 1, 79-84 (January 1989)
··· Sommargren, G. E., and H. J. Weaver, "Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern," Applied Optics, 29, 4646-4657 (1990)
··· Sommargren, G. E., and H. J. Weaver, "Diffraction of light by an opaque sphere. 2: Image formation and resolution consideration," Applied Optics, 31, 1385-1398 (1992)
·· Harrison, M. E., C. T. Marek, and J. D. White, “Rediscovering Poisson’s spot,” Physics Teacher, 35, 18-19 (January 1997)
· Higbie, J., (letter) “More on Poisson’s spot,” Physics Teacher, 35, 197 (April 1997)
· Wong, R. D., (letter) “Still more on Poisson’s spot,” Physics Teacher, 35, 197-198 (April 1997)
··· Wein, G. R., “A video technique for the quantitative analysis of the Poisson spot and other diffraction patterns,” American Journal of Physics, 67, No. 3, 236-240 (March 1999)
·· Kolodziejczyk, A., Z. Jaroszewicz, R. Henao, and O. Quintero, “An experimental apparatus for white light imaging by means of a spherical obstacle,” American Journal of Physics, 70, No. 2, 169-172 (February 2002)


6.157  Halloween physics
Jearl Walker
October 2006
   To celebrate Halloween (well, more to the point, to scare small children senseless), Americans transform pumpkins into Jack O'Lanterns. Triangular eyes and nose and an elongated mouth with a few sharp teeth are cut into the side of a pumpkin, and then a top section is cut out so that the seeds can be removed and a candle can be mounted inside the pumpkin. At night, the candle is lit so that the light escaping through the eyes, nose, and mouth give the glowing impression of a demon, as in this photo by nessman.
    A practical question often arises: Should the top section be put back in place, or should it be removed so that the candle does not burn its underside, creating a stink? From a recent study by Whitehead and Mossman of the University of British Columbia, we can answer that question with some physics.
    The Jack O'Lantern is a gothic version of an integrating sphere---a sphere with a reflecting interior and a small exit port. Such a sphere can be used to measure the total light output from a source, which is mounted inside. If a source emits light in many directions, measuring the total output is normally difficult. However, with the source inside the sphere, the light is effectively trapped except for a predictable fraction that escapes through the exit port. By measuring that escaping amount of light, you can easily determine the total light output from the source.
    In a Jack O'Lantern, the exit ports are the carved-out facial features. Usually enough light escapes through those features to rival the brightness of a full Moon, which is, of course, just right to scare children on a dark night. However, the scare effect is almost eliminated if you remove the top piece, because then too much of the light escapes through the open top instead of reflecting around the interior and escaping through the facial features. The features are then just a dull glow.
   None of this would matter if the interior of a pumpkin did not reflect so well, because then the light would just be absorbed by the interior. A dark Jack O'Lantern on a dark night wouldn't scare anyone.

· Whitehead, L. A., and M. A. Mossman, “Jack O’Lanterns and integrating spheres: Halloween physics,” American Journal of Physics, 74, No. 6, 537-541 (June 2006)


6.158  White beetles
Jearl Walker
March 2007 
  My blue shirt is blue because of pigmentation; that is, the fabric holds certain molecules that absorb in the red end of the visible spectrum, allowing the blue end to be reflected by the fabric. The top surface of a Morpho butterfly wing is iridescent blue because wavelengths of blue light undergo constructive interference when they reflect from the terrace-shaped structures on the wing. That is, those wavelengths leave the wing in step with one another and thus reinforce one another. Other wavelengths of visible light leave the wing out of step with one another and thus cancel one another. One or both effects color other colored surfaces, but what “colors” a white surface, such as the surface of milk? Milk is white because all the colors in the visible spectrum scatter equally well from the various particles in the milk. So, white light goes in and white light comes out. Is something similar responsible for the brilliant white of Cyphochilus beetles, which is a very rare coloration among beetles and other animals?
     Recently Pete Vukusic, Benny Hallam, and Joe Noyes (of Exeter University in Exeter UK and Imerys Minerals Limited in Cornwall UK) attributed the whiteness to the internal structure of the very thin scales on the beetle. Each scale is partially filled with cuticle-like filaments that scatter all the wavelengths in visible light equally well. Were the scales fully filled with the filaments, light could scatter only on the surface, which would give just a dull white. Were the scales barely filled, not much light would be scattered back out of them and they again would be just a dull white. The scales seem to be filled just right for lots of light to be scattered to back to the observer from the interiors, producing the intense white seen on the beetles.
    The white is much whiter than human teeth, where the incoming light is scattered by crystals in a shallow layer on the enamel. Since very white teeth are a fashion trend in many countries, perhaps the teeth could be coated with thin layers resembling the scales on the beetle. Well, maybe. A smile might then be like the headlamps of an oncoming car, which would be more a threat than a fashion statement.

Abstract of the paper:

Photos and news releases:

· Vukusic, P., B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science, 315, 348 (19 January 2007)
· Perkins, S., “Microstructures make a beetle brilliant,” Science News, 171, No. 5, 78 (3 February 2007)
·  “Snow, teeth, paint…nothing is whiter than this beetle,” New Scientist, 193, No. 2588, 16 (27 January 2007)


6.159  Wet tee-shirt (T-shirt) and sunburn
Jearl Walker
August 2007 A common white cotton tee-shirt (T-shirt) is white because the fibers strongly scatter light for any wavelength in the visible range. So, if white light travels into the spaces between the fibers, most of the light reflects once or twice from the fibers and then comes back out. If you intercept this scattered light, you see a white shirt.

If the shirt becomes wet, it is then darker. Now water occupies the spaces between the fibers, held in place by surface tension (the collective force between water molecules and between the water molecules and the fibers). When light reaches an airwater interface, most of it is transmitted into the water. With the water between the fibers, much of the light continues deeper into the fabric rather than just be reflected back out. So, now you intercept less light from the shirt, and thus the shirt is darker.

Ok, how about ultraviolet light? How about the danger of being sunburned by the ultraviolet light? If you wear a dry tee-shirt on the beach, surely it scatters most of the incident ultraviolet light outward and thus prevents it from reaching your skin. But does that protection decrease dramatically if the shirt becomes wet because the outward scattering decreases just as it does for visible light? Are you then dramatically less protected once the shirt becomes wet? Is there truth in the common claim that a wet shirt offers no protection?

Richard Bartels and Fred Loxsom of Trinity University in San Antonio, Texas, investigated the scatter and transmission of light by tee-shirts. Although they considered three types of cloth, I’ll just consider the 100% white cotton cloth that make up the rock-and-roll tee-shirts that I wear. The researchers initially considered the wavelength range between 250 nanometers and 400 nanometers, which contains the dangerous ultraviolet regions of UVB (280 nanometers) and UVA (340 nanometers) that can cause sunburn and skin cancer. They found that wearing a dry tee-shirt greatly decreases the amount of ultraviolet light reaching the skin. A wet tee-shirt does also but not quite as well. So, if you want protection, wear a tee-shirt, even if it is wet.

When they also investigated the visible range of light, they found something that surprised both them and me. The fraction of ultraviolet light penetrating a wet tee-shirt is much lower than the fraction of visible light penetrating it. That is, the wet tee-shirt shields against ultraviolet light far better than it does visible light.

The reason is that a white tee-shirt contains a laundry “whitener.” As I explain in The Flying Circus of Physics, most laundry detergents leave a fluorescent brightener (the “whitener”) in clothing to offset the detergent’s tendency to give a yellow tint to the clothing. The molecules in the brightener absorb ultraviolet light and then emit blue light, a process known as fluorescence (to absorb energy at one wavelength and then to emit it a different wavelength). That extra blue offsets the yellow tint, and you then see the full visible spectrum equally well, which gives you the perception of white.

The point here is that the brightener left in the fabric by the detergent (or put in by the manufacturer) absorbs a lot of the ultraviolet light. So, if you want protection against UV, not only should you wear a tee-shirt, but you should wear a freshly laundered tee-shirt, and then it does not matter very much whether it is dry or wet.

Bartels, R., and R. Loxsom, “The sun-protection factors of wet and dry T-shirts,” Physics Teacher, 36, No. 2, 86-89 (February 1998)

6.160  Glare off a printed page
Jearl Walker
Oct 2008
Look at a page from a shallow angle when it is strongly illuminated by a light source, also at a shallow angle. Then adjust the tilt of the page. You will probably find that in a certain narrow angular range, the bright and dark regions on the page are reversed in contrast. That is, the dark regions, such as the printed words or a dark part of a photograph, become brighter than the white portions of the page. A similar reversal also occurs with a page of penciled notes.

My son Patrick Walker brought this observation to me with the question, “What causes the contrast reversal?” To examine the effect, I took a series of photographs of a homework page in my textbook while it was horizontal and directly illuminated with sunlight at an incident angle of about 40º from the vertical.

The first photograph looks down on the page from 20º from the vertical, catching light reflected from the page up into the camera. The second photograph is at angle of 40º
from the vertical. If the page were a mirror, an image of the sun would appear where the penguins appear, except that we can now hardly see the penguins. The third photograph is from a view at a greater angle to the vertical. Note that the penguins are again distinguishable.

First note that the white regions of the page do not change much as the camera angle changes. Normal writing paper has a fairly rough surface formed by fibers. When light illuminates such paper, the light is scattered almost evenly in all directions, a situation known as diffuse reflection.

To get a smoother surface for quality reproduction of color photographs, textbook and magazine paper contains a filler (usually the white clay kaolin) to fill the spaces between the fibers. The paper still gives diffuse reflection but may also give a specular (mirror-like) reflection at a certain angle of view. You may have noticed this extra reflection when reading a glossy page in a room with many overhead lamps because the glare of the mirror-like reflections of the lamp light may have made the page difficult to read.

The paper used in the current edition of my textbook does not display glare but the ink used in the words, the figures, and the photographs does display glare. If you read the page at the normal viewing angle (photograph 1), you see diffuse reflection from the ink. Where the ink is black, most of the light that penetrates into the ink is absorbed, leaving that section of the page darker than the white, uninked sections. From a view at a shallow angle (photograph 3), the ink still provides only diffuse reflection. However, if you view the page at the mirror-reflection angle, you intercept the specular reflection from the surface of the ink. Even where the ink is black, the specular reflection from the surface can be brighter than the surrounding white areas of the page. This is the effect my son saw --- the normally dark regions are now brighter than the white regions on the page, a contrast reversal.

Light is a wave of oscillating electric and magnetic fields. We usually describe the electric fields and draw arrows (vectors) to represent the strength and direction of the field at any given point and at any given time. The vectors are always perpendicular to the light’s direction of travel, which is usually drawn as a ray, as in a ray of sunlight. The vectors are perpendicular to the ray but they can be in any direction in the plane perpendicular to the ray. Such light is said to be unpolarized, meaning, there is no set direction to the vectors.

However, when unpolarized light undergoes specular reflection from a surface, the light can become polarized, with the electric field vectors restricted to being parallel to the surface. You can check for such polarization by using a polarizing filter, such as a lens in polarizing sunglasses. Indeed, the higher prices commanded by such sunglasses are because they block the polarized glare in the sunlight reflections from roadways and open bodies of water. That is, the glasses will pass (transmit) light that is polarized vertically (the electric vectors are up or down) but they block light that is polarized horizontally (the electric vectors are left or right). Since the reflecting glare has left and right vectors, the glasses block the glare.

In my photographs, the sunlight illuminating the textbook page is unpolarized but the light reflected by the ink is polarized.

Photograph 4 here shows the book page with a polarizing filter over the camera lens. The filter is oriented so as to pass the left-right electric vectors in the glare from the ink. The penguins are difficult to distinguish from the white regions of the page. Photograph 5 shows the page with the filter oriented so as to block the glare light. Now the penguins are distinguishable again because they are darker than the white regions.

You can see these effects of glare and polarization in all textbooks and magazines with good quality paper. Physics is everywhere, even in the printed material about, say, the social history of gardening.

· · 
Harrison, V. G. W., Gloss: Its definition and Measurement, Chemical Publishing Co, Inc., 1949.

6.161  Gun sights and quark transformations
Jearl Walker
April 2010   To allow easier aiming, especially in dim lighting, some handguns and rifles are equipped with gun sights containing the radioactive element tritium, which is a hydrogen isotope. As you can see in this photo of a hand gun by Wikiphantoms, the tritium parts of the gun sights produce three green dots, one on the front sight and two on the rear sight. To aim, a person holds the gun so that the three dots are level, with the front dot equally spaced between the outer two.

The nucleus of the common isotope of hydrogen contains only a proton. The nucleus of the isotope deuterium contains a proton and a neutron. And the nucleus of the isotope tritium contains a proton and two neutrons. Tritium is radioactive in that it will decay when one of its neutrons transforms to a proton, which produces an electron and a neutrino. 

       neutron --> proton + electron + neutrino


(To be precise, the neutrino is really an electron antineutrino but we don’t need that distinction here.) The new proton remains within the nucleus, which now contains two protons and the remaining neutron. (Because the nucleus contains two protons, it is an isotope of helium.) The electron and the neutrino that are created in the decay (they did not exist previously) leave the nucleus. Neutrinos only rarely interact with matter, so the neutrino most likely heads out into space, even if has to travel through Earth. (It is rather like me at a party --- I just don’t readily interact.) The electron, however, almost immediately collides with anything around it, dumping its kinetic energy into the material.

A tritium gun sight holds many small glass vessels of tritium gas. The electrons emitted by the tritium decays collide with a surrounding phosphor layer. The transfer of energy from them into the phosphor molecules excites the higher energy levels. They quickly then de-excite by emitting light --- the green light that you see in the photo.

The decay of tritium is a random event, that is, it occurs spontaneously without any warning or cause. If there was only one tritium nucleus in a gun sight, we would get a single flash of light at some random time in the next several years. Of course, that would be useless. So, the dots on each site contain many tritium nuclei so that, at least to the human eye, decays happen almost continuously and the light is steady. The gun sights are appreciated by both gun enthusiasts and the military because they provide illumination without batteries and without any upkeep for many years.

Because of that freedom from electricity, tritium that is encapsulated in glass coated with phosphor is also used in watches, exit signs, and aircraft control boards. Although you might worry about the radiation exposure, the neutrinos completely ignore you and the electrons are so low in energy that they cannot penetrate skin. However, if you were to ingest one of the tritium devices, you might have a problem. Of course, you are not going to eat one, but if a great many of the capsules were to burst near you, you might inhale the gas. Then the electrons would be stopped by your lungs.

My explanation of the decay process above about the decay involving a neutron transforming to a proton is the standard one. Let me go one step deeper in the explanation. Neutrons and protons each consists of three quarks, the “particles” that are bound up to form the group of fundamental particles known as hadrons. The common quarks (that is, the ones inside the protons and neutrons in your body and everything around you), are the up quarks and the down quarks. (The names may be whimsical but the physics is real.) A neutron has one up quark and two down quarks, 

                      neutron = (up + down + down) 

whereas a proton has two up quarks and one down quark  

                      proton = (up + up + down). 

So, when I say that the tritium decay involves this transformation 

                 neutron  --> proton + electron + neutrino,
what I really mean is that one of the down quarks in the neutron is spontaneously transforming to a up quark: 

     (up + down + down) --> (up + up + down) + electron + neutrino. 

Thus, we have a rather startling connection. If you sight a gun with a tritium sight, tell the time with a tritium watch, or fly an airplane with a tritium console, the illumination you see is ultimately due to the quark transformations within the nuclei.

6.162 Relativistic length contraction---what does it look like?
Jearl Walker
July 2010   One of the non-intuitive consequences of Einstein’s special relativity is length contraction --- when an object moves relative to you, its length along the direction of motion is shorter than when the object is at rest relative to you. That at-rest-length is called the proper length. Relative motion causes the length to decrease, and the greater the relative speed is, the shorter that length becomes. Such shortening is not commonplace (nor common sense) because it is not appreciable unless the speed is at least 10% of the speed of light.

The contraction is real, not an illusion or error and has been experimentally verified by countless experiments using high speed particles, both in research labs and student labs. If you have taken a course in special relativity, you know that to calculate the contracted length, you divide the proper length by the square root of (1- v2/c2), where v is the relative speed and c is the speed of light.

You also know that in making such a calculation, you are finding the length of the object as measured on a three-dimensional grid of measuring rods and small clocks, along which the object is moving.

Suppose a meter stick is moving very rapidly along the x axis of the grid. To measure the length of the stick, the locations of its two ends are simultaneously marked on the nearest measuring rod.

Then, at our leisure, we can find the distance between the two marks, to give us the measured length of the stick, finding that it is less than 1 meter.

We use such a grid to avoid having to determine how long a signal takes to travel from either end to us. For example, if the signal is light, then we would have to wait a certain amount of time for the light signal from the rear of the stick to reach us and a different amount of time for the light signal from the front of the stick. We could still find the contracted length by subtracting out the travel times, but the calculation would be messier.

The calculation gives us the measured contracted length of the object, but what would the object actually look like to our eyes or, more realistically, to a high-speed camera? About 50 years after Einstein published his theory, physicist James Terrell considered what a high-speed image would capture --- it would not be simply a contracted object as we would measure. The difference is that an image is made by all the light that arrives at the instant the image is made, but those light rays would have to leave the object at different times because of the different distances from various parts of the object to the camera.

Terrell described the image as one in which the object is rotated --- the image shows a shortened object but we also see the rear end of the object, as if the object were rotated around the y axis. The object is not actually rotated. We see the rear end only because the image captures light emitted earlier by the front of the object and light emitted later by the rear of the object. The composite seems wrong because it shows the perspective of the rear end that is inconsistent with the perspective of the front, and we interpret the composite as being that of a rotation.

In 2005, Robert J. Deissler, then of Cleveland State University, worked out equations that would transform an image of a stationary object into what would be seen in an image of the object when it passed a camera at a relativistic speed. Here are some of his examples, with the object being him on a skateboard. First, here is his stationary appearance, with the camera pointed perpendicular to the skateboard.

For a speed that is 90% that of light speed, here is the appearance as would be calculated by the routine equation for contraction (or measured along a grid of rods).

For that speed, here is the appearance as would be captured in an image by a high-speed camera.

Deissler and his skateboard are contracted in the direction of motion but the contraction is difficult to see because of an apparent rotation around the vertical --- we see the rear side of Deissler. Notice, however, that the skateboard is still pointed down the hallway. Deissler pointed out that the effect is better described as being due to shearing rather than rotated because there is also a curvature to his body, with the head and feet curved toward the rear.

If you want to watch two videos that I produced for the web material associated with my textbook, go to the Facebook site for The Flying Circus of Physics at!/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=wall&ref=ts

and click on the videos posted on July 1. First watch “The Relativity of Time” in which I derive the time dilation equation using only algebra and Einstein’s original example. Then watch “The Relativity of Length” in which I use only algebra and the time dilation equation to derive the length contraction equation.

If you are a physics instructor, you might be interested in the web-delivery system (Wiley Plus) that is associated with my textbook, Fundamentals of Physics by Halliday Resnick, and Walker. The system for the ninth edition of the book contains

· the electronic copy of the textbook

· animation videos of one of the key (but complicated) figures in each chapter --- in the animation I talk the students through the main points of the figure

· 200 of my tutorial and math review videos

· 334 of my sample problem videos, a video for every sample problem in the book

· 700 of my video solutions to the homework problems (these are available to the students at the discretion of the instructor)

· homework grading system for all 6000 homework questions and problems in the textbook, plus more problems that are not in the textbook. At the discretion of the instructor, each problem is linked to the associated text material, my sample problems, and my videos and also to simulations and video demonstrations.

· brief hints on each of the homework problems (at the discretion of the instructor)

· over 500 tutorials that I have written in which a student works through a homework problem in steps, with hints given when wrong answers are submitted animation of a flyby of a city simulation of contraction animation animation about time dilation the two postulates of relativity

··· Terrell, J., “Invisibility of the Lorentz Contraction,” Physical Review, 116, No. 4, 1041-1045 (15 November 1959)
··· Penrose, R., “The apparent shape of a relativistically moving sphere,” Proceedings of the Cambridge Philosophical Society, 55, 137-139 (1959)
· Weisskopf, V. F., “The visual appearance of rapidly moving objects,” Physics Today, 13, No. 9, 24-27 (1960)
·· Scott, G. D., and M. R. Viner, “The geometrical appearance of large objects moving at relativistic speeds,” American Journal of Physics, 33, 534-537 (1965)
·· Scott, G. D., and H. J. van Driel, “Geometrical appearances at relativistic speeds,” American Journal of Physics, 38, No. 8, 971-977 (August 1970)
··· Hickey, F. R., “Two-dimensional appearance of a relativistic cube,” American Journal of Physics, 47, No. 8, 711-714 (August 1979)
··· Suffern, K. G., “The apparent shape of a rapidly moving sphere,” American Journal of Physics, 56, No. 8, 729-733 (August 1988)
··· Burke, J. R., and F. J. Strode, “Classroom exercises with the Terrell effect,” American Journal of Physics, 59, No. 10, 912-915 (October 1991)
··· Deissler, R. J., “The appearance, apparent speed, and removal of optical effects for relativistically moving objects,” American Journal of Physics, 73, No. 7, 663-669 (July 2005)
··· Cavalcanti, C. J. de H., F. Ostermann, “Apparent geometrical deformations and superluminal velocity on objects in relativistic motion,” (Portuguese) Revista Brasileira de Ensino de Fisica, 29, No. 3, 355-372 (2007)

6.163  “Powers of Ten” --- the video
Jearl Walker
Nov 2010  One of the most powerful (and humbling) films ever produced is the one released by designers Ray and Charles Eames in 1977. It begins with an overhead view of a man napping at a picnic in Chicago, and then the camera moves away from the man at the rate of one order of magnitude of distance every 10 seconds. That is, every 10 seconds the distance between us and the man is 10 times greater:

1 meter initially at time = 0
10 meters at time = 10 seconds
100 meters at time = 20 seconds
1000 meters at time = 30 seconds
and so on  YouTube video web home of the video and news about the 10-10-10 events

Initially we see the rich details of the picnic and the surrounding grounds, but such sights of civilization soon become irresolvable, and we begin to see the planet itself and then the nearby portion of the solar system. Soon the solar system grows too small in our view and the sun dims to be just another star. All signs of what we are as humans and where we belong have now disappeared.

As we back out of the plane of the Milky Way galaxy, we see the vast number of stars that make up the galaxy. As the Milky Way grows smaller and then disappears, along with the local cluster of galaxies, we move into the vast nothingness of deep space, with hints of clusters and superclusters. Nothing then changes and we stop our journey.

Even if we were to continue, nothing new would happen, no mater how long we traveled. At this scale, the universe is pretty much the same everywhere. Although the total volume of the universe is finite and not infinite, there is no “wall” or surface to the universe. That volume is continuously increasing, not because the material in the universe is racing out into existing empty space, but because space itself is continuously coming into existence between the clusters of galaxies.

In the movie, after the brief rest, we reverse the outward journey and, when we again see the napping man, we plunge into his hand, down through the flesh and into a vein and then into DNA, and then in carbon atom until we see the nucleus of the atom. This inward journey has also been at the rate of an order of magnitude every 10 seconds:

1 meter initially at time = 0
0.1 meter at time = 10 seconds
0.01 meter at time = 20 seconds
0.001 meter at time = 30 seconds
and so on


When the movie was made, no one could take images of molecules and atoms and thus the move’s renditions of them are just animations. Now, with instruments such as scanning tunneling microscopes, not only can we take images of atoms and molecules, but we can move the atoms and molecules around to form novel patterns or spell out a logo or word.

The movie ends with the narrator hinting that the nucleons (protons and neutrons) in a nucleus consist of quarks. Although quarks had been proposed and experimentally verified by the time the movie was made, they were still not universally accepted by the physics community. These days we are quite certain that protons and neutrons consist of three quarks each and also gluons (the particles that are responsible for holding the quarks together).

The entire journey from the outermost point to the innermost point covers 40 orders of magnitude, that is, 40 zeros. We understand the physics over at least that extent. If you include the universe itself, the extent is even larger.

Phil Morrison
The 1977 Powers of Ten was narrated by Philip Morrison, who was a physics professor at MIT, a book editor at Scientific American, and the smartest person I ever met. (Someone once told me that we could give Morrison a list of 10 terms taken from any region of study in science or liberal arts (history, philosophy, etc.) and he would be able to talk about each term for at least half an hour. When he read books for review in Scientific American magazine, he would speed-read the books, with a few seconds per page. He did not need to read to learn the subject. He already knew it thoroughly. He merely wanted to see what the author chose to put in the book.

When I wrote the early material of The Flying Circus of Physics in graduate school, I sent a copy to Morrison. I realized that this was foolish because I was only a student and Morrison was a famous physicist, and the stuff I sent him was amateurish. To my astonishment, Morrison wrote back, suggesting that I publish the material as a book. Because of him, because of his taking the trouble to respond to a mere student in another university, I took the bold step to ask a publisher if The Flying Circus of Physics could be published as a book. Because of Phil Morrison, a domino effect of events then occurred, bringing me to this point in time.)

Earlier versions
Powers of Ten first appeared as a black-and-white movie in 1968 (with a female narrator) and was based on a 1957 book Cosmic View by Kees Boeke. A similar movie, Cosmic View, also appeared in 1968, also inspired by the book.

Cosmic zoom Eva Szasz, 1968, 8 min, National Film Board of Canada.
Also at

Both Powers of Ten and Cosmic Zoom have been imitated many times, especially with today’s high tech video software that can be used in, say, in an art class. A few such videos are linked below.

Here is an idea. Anytime your day’s events become overwhelming, play one of these videos to see just how tiny your daily world and its concerns are in the grand scheme of things.

Power of 10 – Perspective on the Universe

Powers of Ten Zoom Out very pretty

From Quarks to Outer Space


6.164 Audience scanning
Jearl Walker
March 2011  Audience scanning is the practice of sending laser beams directly into the audience at a concert.

Commonly, the beams are swept rapidly across the eyes of the audience members to create a psychedelic atmosphere or to give the illusion of being in a tunnel or cone of light. Less common, the audience members use laser pointers to light up the dark auditorium, with the beams being reflected back into the audience by mirror-like objects. Here are three links to concerts by The Flaming Lips that demonstrate both types of audience scanning. laser beams sent into the audience holding up a mirror to reflect the beams back into the audience laser pointers gone wild

Lasers and rock

Lasers were invented in 1960 and started appearing in rock shows in the mid 1970s. The first time I saw them in a concert was at a Genesis show in 1976. They were stunning and beautiful, bright beams of pure color that sliced through the air over the stage and over the heads of the audience, moving and weaving in time to the beat of the music. The purity of the individual colors is a characteristic of laser light. Whereas a common light bulb emits at all wavelengths in the visible range, a laser emits light in a very narrow range of wavelengths, thus giving an almost pure color.

Although a laser beam can be very bright (its emission power, or the amount of energy emitted per second, is large), the beam is not necessarily visible to an observer unless the beam is directed into the eyes. The problem is that in order for you to see the light from the side, at least some of the light must be scattered from the beam to you. If the laser beam shines on a surface, part of the light will be reflected to you. You may not see the beam itself, but you can see a bright spot on the surface.

To see the beam itself, there must material in the air to scatter some of the light to you. Such scattering is strongest in the forward direction (the direction the light is traveling) and in the rear direction (back toward the laser). In the Genesis concert, I could easily see the beam even when my view was perpendicular to it. The strong sideways scattering was due to the thick smoke in the auditorium air from the smoking of cigarettes and (probably) marijuana.

A few years later I attended a laser show that featured the music of Pink Floyd. The show was given in a hemispherical tent that was sent up inside a local auditorium. Here the beams were used to illuminate the underside of the tent ceiling, moving rapidly over the surface so as to create geometrical designs and sweeping displays of color in time with the music. Only one beam was used but it moved so rapidly over the tent surface that a figure was seemingly was drawn instantaneously. By shifting a figure from moment to moment, the figure appeared to move over the surface.


Audience scanning

The first occurrence of audience scanning was reportedly in a 1976 concert by the now legendary heavy metal band Blue Oyster Cult during their Agents of Fortune tour. A physicist was positioned off to one side of the stage, out of sight by the audience. He directed a laser beam onto the shiny guitar of the lead guitarist, who then rotated the guitar so as to scan the reflected beam across the audience. In the jargon of laser physics, a powerful “raw” beam swept across their eyes.

The beam surely reached the retinas of the audience, but no claims of retinal damage (or lawsuits) were filed. However, the incident prompted investigation by the federal government, who then sent an agent to some of the other BOC concerts on that tour. For a while, the band was not allowed to scan the audience, but as you can see in this old television documentary the technique was merely changed. The laser was still off stage but the light came to the lead guitarist through optical fibers that snaked up his clothing and out along his arm. At a dramatic moment in the music, with the lights in the auditorium low and the guitarist pointing upward, the laser was switched on and the beam seemingly erupted from his outstretched finger. He could then direct them at an overhead rotating disco ball (with many small flat mirrors on its side) to reflect the beam across the audience. Or he can lower his hand and swept the beam across the audience directly.

Since then, regulations have been set world wide for the use of lasers in concerts and other displays. In particular, there is a “maximum permissible exposure (MPE)” on the lasers --- the level expresses the greatest amount of energy to which a viewer can be exposed “safely.” (Here, of course, experts could argue about what “safely” actually means.) In the United States laser-display companies faithfully adhere to this limitation but in other countries the enforcement of the limitation is reportedly lacking. In Europe, for example, exposure in a rave or nightclub might be 10 or even 100 times the MPE. The demand for brighter laser display might partially be due to the banning of smoking inside concert halls or rave centers. If the air contains only a little bit of dust and perhaps some smoke from a theatrical smoke machine (perhaps small water drops), then seeing a weak beam from the side is unlikely.

Arguments are now being made to raise the limit in the United States, provided the audience is warned of the danger before being exposed to the laser beams. (The argument pivots on the idea that the audience is already choosing to endanger themselves if alcohol is being served. So, why not also expose them to bright lights?) Actually, calculating and measuring the maximum safe level is safe is difficult because you must include the rate at which beam travels across the eyes, the focusing of the light on the retina by the eye, the spreading of the laser beam with distance, the spreading that occurs if the beam is sent through, say, slightly frosted glass, the effect of different wavelengths on the retina, the expansion of the iris in the normally dim light of a concert room, the tendency of the eyes to blink in bright light, and the tendency of the viewer to avert the eyes when seeing light. I think the (strong) possibility of drug use by the audience should also be a consideration, because some drugs tend to expand the iris of the eye, allowing more light to enter the eye.

In general, lasers come in two types: continuous (the light is continuously emitted) and pulsed (repeated, intense bursts are emitted). The rule among the companies that put on laser light shows is that only continuous lasers should be used because they can be at a fairly low power. The pulsed lasers might also seem to have a low power if you average the energy output over a long period (during a pulse and also the down time), but during each individual pulse, the energy output can be quite high. If an eye intercepts such a pulse as the beam sweeps across someone’s face, the high energy on the retina can damage the retina.

According to news reports, a pulsed laser was used at an outdoor festival near Moscow in 2008. Because of rain, the crowd was gathered under a large tent. The powerful laser was scanned across the audience and reflected from the ceiling of the tent. Afterwards, approximately 60 audience members reported for medical treatment for their eyes. Initial reports claimed severe retinal burns, but I cannot confirm that. Had the laser been directed upward through the night air (and perhaps onto the base of a cloud), the display would have been spectacular but safe. CBS news footage (no narrative) news report on Russian television


The new, powerful laser pointers

Originally, lasers were large and bulky and often depended on long tubes of one more gases being made to lase. But modern solid state lasers (laser pointers) are relatively small (pocket sized) and portable and can be plugged into a common wall outlet or simply battery powered. Recently inexpensive and small green lasers (using indium gallium nitride) have been added to the traditional blue lasers (gallium nitride) and red lasers (aluminum indium phosphide).

The material in front of your retina is fairly transparent to visible light, from the blue end of the visible spectrum to the red end. In addition, the light is focused by the cornea and the lens, concentrating the light onto the retina. When the intensity is too high, that focused light can damage or destroy the retina. At the blue end, the damage is due to overloading the chemical changes that blue light creates in the retina. At the red end, the damage is due to overheating the retina. The damage could be in spots or, if the beam travels across the retina, the damage could be along a line.

Someone with retinal damage might not even be aware of it because the brain naturally fills in missing sections of what is being viewed. Indeed, you have a blind spot in each eye where the optic nerves are connected to the retina. Your brain readily fills in that blind spot, extrapolating from what is being seen around the spot.

Most laser pointers are low-power solid-state lasers that are considered to be safe for use in classrooms and lectures. Traditionally such “Class 1 lasers” have an output power of about 5 milliwatts or less. Although the beam would be focused down to a small region on the retina, the focused energy is not absorbed fast enough to overheat or overload the retina. (Nevertheless, you should never expose your eyes directly to the beam of a laser pointer. If you ruin your eyes, there is no “do overs” or “game reboot.”)

Although the traditional laser pointers were considered to be safe, recently new, far more powerful laser pointers have appeared for purchase on the web. The more powerful ones appear to be the green laser pointers, which have output powers of 15 milliwatts or more. The laser pointer shown here is rated at 500 milliwatts!

I have seen one of the new green lasers --- the spot it produced on a chalk board was too bright for me see for more than a glance. Safe exposure to light from a Class 2 laser is limited to 0.25 second. The green laser I saw was much brighter and would surely burn my retina almost immediately if my eye intercepted the beam directly.

So, how about the laser pointers used at the Flaming Lips concert? Maybe they were all Class 1 lasers and there was no real danger. But how could the audience members tell? How did they know that someone had not pulled out a Class 3 laser just to show off and was bouncing the beam off that floating, reflecting balloon or off the mirror the band member held up on stage?

In general, if you are at a concert where lasers are sent into your eyes, I suggest that the best thing to do is to enjoy the music with your eyes closed. After all, if someone has made an error in the laser choice (as in the Russian festival), if the computer program controlling the laser freezes up and holds the beam on your eyes too long, or if various other things go wrong, you could lose your sight. Then hearing a concert is all that you are going to be able to do at a concert.

 More links

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Chellappan, K. V., E. Erden, and H. Urey, “Laser-based displays: a review,” Applied Optics, 49, No. 25, F79-F98 (1 September 2010) Photonics article from 24 July 2008 about the Russian incident


6.165  Wooden mirrors
Jearl Walker
December 2012 Here is an array of computer-controlled wood slates that functions as a mirror. As you might guess, the slates are varnished and thus are fairly reflective, just as with any bare-wood wall. But if you stand in front of such a wall, you certainly cannot see an image of yourself that is distinct enough for you to, say, brush your hair.

In contrast, the array of slates, which is an example of kinetic art, is different as demonstrated in the following video. A small video camera is mounted at about eye level in the middle of the array and continuously records whatever is in front of it.

Let’s assume that you are standing there. Your recorded image is split up into many sections, one for each of the wood slats. The intensity of the light in each section is measured, and then each slat is rotated around a horizontal axis to adjust how much light it reflects from overhead. If a certain section of your image is bright, then the corresponding slat is rotated upward so that the slat reflects lots of the light out to you and any other viewer. If, instead, an image section is dim, then the slat is rotated downward to reduce the reflection of the light toward a viewer.

The result is that the array becomes a mosaic, with the composite brighter and dimmer slates creating an image of you.

You have seen such mosaics before, in art works and advertising. If you stand close to the mosaic, you might see hundreds of small images. But if you stand farther back, you cannot resolve the individual images but instead you see some completely different image formed by the brighter and darker regions. Here is an example (it takes a bit to load). If you click on the picture of an eagle, you zoom in and then can see that it consists of photographs taken at parties and other gatherings.

This mosaic is from . Here is another site that will help you create photo mosaics on your computer:

The term photomosaic was trademarked by Robert Silver, whose web site is.

Click on one of his art works to see the individual images forming the art.

More links: mosaic blog

1.66  Pub trick --- water from nowhere
Jearl Walker
March 2015 

My question here is simple and obvious: How does water appear from nowhere in this video, in which water is poured from a small glass container into progressively larger empty containers, but we end up with far more water than in the initial container.

Of course, water cannot appear from nowhere. There must be a conservation of mass in the simple process of pouring water, so how do we end up with far more water than we had initially?

Note that the water in the initial glass container was visible only because a bit of milk had been added, so that we see a white, milky liquid. Without the milk particles to scatter light to us, we could not have seen the transparent water, especially with the textured sides of the container. How about the second container? We assume that it is empty and thus are surprised that the small volume of milky water from the first container could fill it. However, the second container already had enough clear water so that when the first container is added, the second container is full. The milky stream runs down into the clear water and then the milk suspension spreads throughout the clear water, making the full contents visible.

Thus, we start with a short container of milky water and a series of containers partially filled with clear water that we cannot see. If we were to drop some dye in those other containers, the magic of this trick would immediately disappear.


6.167  Pinhole rifle sighting, pinhole glasses, and pinhole selfies
Jearl Walker
July 2015  With normal vision, a person can clearly see a nearby object and a more distant object, but not simultaneously. To shift from reading a book to seeing a car down the street, I have to adjust the focusing of my eyes, which I do subconsciously by changing the muscle that controls the shape of the lens inside each eye. When I aim a rifle, I need to line up the target (which might be 20 meters down the shooting range) and also the front and rear sights on the rifle, but I cannot see all three things simultaneously --- at least one of them is blurred.

One solution to this common problem is to mount a pinhole device just in front of my shooting eye. By looking through the pinhole I greatly increase the distance through which objects are simultaneously in focus (or nearly in focus). The advantage of the pinhole is that it decreases the angular range of light rays coming from an object and reaching the retina at the rear of the eye.

Suppose I look at a nearby point source of light and a more distant source. If I adjust my eye so that the more distant source is in focus, then light rays from it form a small image on the retina.

However, the light rays from the nearby source then “attempt” to form their image behind the retina.

So, those light rays from the nearby source illuminate a larger region of the retina, and what I see is a fuzzy image of the nearby source.

If I then place a pinhole just in front of my eye, the pinhole allows only part of the light rays from the nearby source to reach the retina. Thus the illuminated range on the retina is smaller and I see a sharper (though dimmer) source.


Pinhole glasses

Pinhole glasses have very dark plastic “lenses” with many pinholes (or tiny clear circles) through which light is transmitted. Suppose a person is far sighted and cannot read a book page. By looking at the page through the pinhole glasses, the letters produce smaller images on the retina and are thus much less fuzzy. This advantage of pinhole glasses has long been known, but unfortunately many false claims have been made about the glasses altering vision in a permanent way so that the person moves toward perfect vision. They do no such thing. For example, this video recommends that you “exercise” the muscles of your eyes for 15 minutes a day by using pinhole glasses. There is no medical evidence that the eyes change.

Pinhole cameras
Pinhole cameras are still popular even though most designs require photographic film, which is no longer common. Still, they are fun and easy to make, even with a small box. A pinhole is punched in one side of the box, with opaque tape placed over the hole. In a dark room, film is then mounted on the inside wall on the opposite side of the box. The box is kept closed and the pinhole is kept covered until a photograph is to be made. Then the tape is removed. Light from the subject can then enter the box and record an image on the film. Experience is needed to know how long the film is to be exposed, but several minutes are usually required because of the low illumination entering the box.

Recently photographic artist Ignas Kutavicious developed a technique of using a pinhole camera to take a selfie (self image). Here you can see him posing with its equipment.

The drawback is that the person being photographed must remain still for as much as five minutes in order to expose the film sufficiently. Here is a gallery of some of his work: Longer description of pinhole sights for rifles


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Baez, A. V., "Pinhole-camera experiment for the introductory physics course," American Journal of Physics, 25, 636-638 (1957)
· Young, M., "Pinhole optics," Applied Optics, 10, 2763-2767 (1971)
·· Young, M., "Pinhole imagery," American Journal of Physics, 40, 715-720 (1972)
·· Young, M., "Zone plates and their aberrations," Journal of the Optical Society of America, 62, 972-976 (1972)
· Walker, J., "The pleasures of the pinhole camera and its relative the pinspeck camera" in "The Amateur Scientist," Scientific American, 245, No. 5, pages 192-200 + 202 (November 1981). Available at
·· Young, M., "The pinhole camera: imaging without lenses or mirrors," Physics Teacher, 27, 648-655 (1989)
··· Hogert, E. N., M. A. Rebollo, and N. G. Gaggioli, "Directional image processing using a pinhole camera with a rectangular aperture," Applied Optics, 30, 1361-1365 (1991)
·· Rabal, H. J., and G. M. Bilmes, "Double-slit camera," Applied Optics, 32, 2219-2221 (1993)
· Jakovidis, G., "A pinhole imaging experiment," Physics Teacher, 31, 500 (1993)
· Cabe, P. A., “A ping-pong ball camera obscura,” Perception, 32, No. 7, 895-896 (2003)
· Cepic, M., A. G. Blagotinsek, and N. Razpet, “Looking through pinhole glasses with a digital camera,” Physics Teacher, 46, No. 3, 186-187 (March 2008)



6.168 Pub trick --- optically reversing arrows
Jearl Walker
October 2015  On paper or card, draw an arrow pointing to the left and, above it, another arrow pointing to the right. Using only materials found in a pub or kitchen, how can you make the arrows reverse their directions (without touching the paper or card)?

The trick is to use a glass of water (preferably with straight sides). Position the glass several centimeters in front of the arrows and then look at them through the water. The water and glass wall act as a lens and invert the arrows in forming a real image on your side of the glass. Here is a sketch of two light rays that leave the ends of an arrow, pass though the water-glass lens, and then emerge to a viewer’s eye.

And here is a video:

You can experiment with the positioning of the glass. If it is too close to the arrows, the glass forms a virtual image of the arrows, without any reversal. At an intermediate position, the arrows are in the focal plane of the water-glass lens and no distinct image can be seen.

When the glass is empty, the arrows are not reversed because the glass only slightly alters the paths of the light rays to you.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Gardner, M., “Reverse Jack’s profile,” The Physics Teacher, 37, 318 (May 1999)

6.169  Black egg becomes glimmering
Jearl Walker
November 2015  In this video, an egg is covered with black soot from a small candle flame and then put into water. Once in the water, the egg’s edge glimmers, an appearance that some people say is silvery.

So, how can a very black surface have a glimmering edge? Here is a video showing the egg preparation.

In air, the egg is black because of the soot. That is, the soot absorbs most of the visible light that illuminates it, and thus we do not get much light from the egg’s surface. In water, things are different because the soot repels water --- it is hydrophobic. So, as the egg moves down into the water, a thin film of air clings to the egg’s surface to keep the water away.

That thin film of air changes the way we receive light from the egg. Here is an overhead view of the egg with the air layer exaggerated.

A ray of light from behind the egg reaches the air layer and then refracts into the layer, which means that the light ray bends at the water-air surface. The ray is bent again when it refracts from the air layer back into the water. This double bending sends the light toward an observer’s eye. Thus, the observer sees extra light coming from the right edge of the egg. The same brightening occurs around the full edge of the egg in the observer’s view. So, the edge of the egg glimmers with extra light.

6.170 Retroreflecting antlers on reindeer
Jearl Walker
March 2016 Approximately 4000 vehicle-reindeer collisions occur each year in Finland. Not only are animals usually killed or severely hurt, but vehicle occupants may be killed if an animal is flipped up and into the windshield. To decrease the chance of such collisions, an experiment has been run for several years on making the reindeer more visible during the long winter nights in Finland. The antlers are sprayed with a retroreflecting dye, so that when a vehicle’s headlamps shine on them, some of the light is sent back (retro-reflects) toward the vehicle, making the reindeer visible to the driver.

You have seen such retroreflections from common street signs at night. So that a sign is very noticeable in the dark, it is coated with tiny beads. Light passes into the beads and then reflects off the back side, back toward the headlamps on your car.

If the experiment proves helpful there in Finland, the challenge will be to spray the antlers of many of reindeer, which number in the hundreds of thousands. The antlers are shed each spring, and so, each fall, the new set of antlers will have to be sprayed. That will be lots of work, but owning that Finland is the rumored home of Santa Claus, those reindeer need to be protected.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Van Lear Jr., G. A., "Reflectors used in highway signs and warning signals. Parts I, II, and III," Journal of the Optical Society of America, 30, 462-487 (1940)
· Cochran, W. R., "Mirror wall tile and the triple reflector," American Journal of Physics, 50, 765 (1982)
··· Harris Jr., W. S., "The corner reflector," The Mathematics Teacher, 76, 92-93 (1983)
··· Morton, N., "Don't forget the reflector," Physics Education, 26, 243-248 (1991)
· Robb, N. I., "Teaching reflection from a corner cube reflector," Physics Teacher, 29, 255 (1991)
··· Wang, S., E. Bernabeu, and J. Alda, "Retroreflective properties of a hemispherical surface," Applied Optics, 32, 4279-4281 (1993)
··· Grosges, T., “Retro-reflection of glass beads for traffic road stripe paints,” Optical Materials, 30, 1549-1554 (2008)
·· Halstuch, A., and Y. Yitzhaky, “Properties of light reflected from road signs in active imaging,” Applied Optics, 47, No. 22, 4031-4036 (1 August 2008)


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