Tuesday, April 17, 2012

Coille Effect

Frank Crawford playing his corrugahorn
Frank Crawford was a remarkable Berkeley physicist known for his flamboyant popularizations of physical phenomena. He built wave machines in the Sproul Plaza fountain, demonstrated the physics of
bull roarers, whistles and other acoustic noise-makers in public places, sold a musical instrument of his own invention (the corrugahorn) on Telegraph Avenue and authored a classic textbook Waves on wave phenomena.

I met the legendary Frank Crawford only once. In 1960, I was working at the Bevatron at Berkeley's Rad Lab, which was the Large Hadron Collider of its day, where the antiproton had just been discovered using instruments designed partly by Frank Crawford. I was standing next to the Bevatron beam line with a group of other scientists and Crawford spontaneously produced one of the first Aphorisms of Quantum Tantra: "Have you ever wondered, Nick, if we physicists have not all along been looking at Nature's backside?'

Among his many large accomplishments, Frank Crawford is the author of a small masterpiece: a physics paper with a rare measure of gallantry-- Coille Effect: A Manifestation of the Reversibility of Light Rays which appeared in the American Journal of Physics, Vol 41 1370 (1973) and which I reproduce here in its entirety:

One lovely late summer afternoon a friend and I were sitting outside basking in a very large tub of hot water. The afternoon sunlight was fragmented by the branches of a tree into many parallel beams, These beams were refracted at the water surface and gave leafy patterns of sunlight on the bottom of the tub. At the edges of the patterns Coille noticed color effects. With smug erudtion I explained these as being due to the greater refraction of blue than of red light. But that wasn't what she meant. Coille had noticed a peculiarity of the color effects. Depending on where she sat, the patterns either had colored edges or did not! When she sat with the sun coming over her shoulder the patterns appeared perfectly white (or sun-yellow rather). When she faced the sun and looked at the same patterns from the other side of the tub they had colored edges. At first I didn't believe her. How could the color depend on where you sit? Finally I was able to overcome my prejudice and see the effect. Then I didn't believe my eyes.

How can it be that a color pattern produced by refraction can look so different depending on the angle of view and whether one is close to it or not?

The explanation is straightforward and leads to a nice demonstration of the reversibility of the paths of light rays. In the Figure below we see a narrow beam of white (W) light incident along path 1 to 2, striking the water surface at point 2.

The blue (B) component of the white light is refracted more than the red (R) and goes from 2 to 4. Red goes from 2 to 3.

The bottom of the pool is a diffuse reflector. Therefore the points 3 and 4 each constitute a light source sending out light in all directions.

Coille effect in a Berkeley hot tub
Consider an observer whose eye is located near the point 1 and who looks to the pattern of light emitted by the sources at 3 and 4. Because of the reversibility of light rays the path of the red light from point 3 to the obsever at 1 must be along path 3 to 2 to 1. Similarly, blue light from 4 that gets to the observer must take path 4 to 2 to 1.

Thus both red and blue return to point 1 along path 2 to 1, that is, they enter the observer's eye traveling in the same direction along the same ray. Thus the observer sees points 3 (red) and 4 (blue) superposed. They both appear to come from the direction of point 8. Her eye and brain now combine the color spectrum and she sees a white spot on the bottom of the pool.

Now consider what happens when she moves her head from point 1 to point 7. (The light beam is still incident along ray 1 to 2.)

Suppose that the blue light from point 4 travels along path 4 to 6 to 7. What path must the red light take in going from 3 to 7?

If it could go along path 3 to 6 to 7, then the blue and red beams would superpose to give a white spot.

But that would demand that the red light refract more than blue at point 6, whereas we know that the red refracts less than the blue.

Thus the red light takes a path 3 to 5 to 7. The observer at 7 therefore sees red and blue light incident from different directions, and thus sees a smeared-out color spectrum on the bottom of the pool.

Thus we have explained Coille's observation.

In case one has a suitable pool (several feet deep with a smooth water surface) and sunlight, but no foliage to make beams, one can make sunbeams by punching holes in a large piece of cardboard and floating this on the surface of the water.

It is a pleasure to acknowledge the acute observations of Coille Hooven which were the basis of this note.

 NOTE: I have not seen what I call the Coille effect mentioned anywhere. I searched in standard optics textbooks and in that beautiful book by M. Minnaert Light and Color (Dover, New York 1954).

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