PUDDLES AND POOLS DISPLAY several intriguing optical properties. Under what conditions can you see shadows on a body of water? Why are you sometimes able to see your own shadow but not that of a person standing nearby? What produces the bright streaks of light you sometimes see radiating from the shadow of your head on a pool? Why are shadows in a pool often fringed with colors or overlaid with images of the surroundings?

Water displaying moderate waves has a particularly curious property. Suppose you photograph the reflection of the mast of a sailboat. As you might expect, the mast in the photograph will look sinuous and kinked. Parts of it, however, also show up as isolated loops. What produces them? Are they always closed?

I begin with the problem of shadows. A shadow forms on a sunlit surface when an opaque object such as a book keeps light from reaching part of the surface. The rest of the surface scatters light in your direction so that you perceive it as being illuminated and the shadow as being dark. The shadow reproduces the shape of the book. The borders of the shadow are formed by the light rays skirting the edges of the book.

If the sun were a point source of light, so that its rays were precisely parallel, a shadow would be uniformly dark. If you look closely at the shadow of a book held above a sidewalk, however, you will see that the borders are slightly brighter than the interior. The region of partial illumination is the penumbra and the darker interior is the umbra. The penumbra results from the fact that the sun occupies about half a degree in the visible sky. The rays passing the edges of the book are spread through an angle of that size. Some of them illuminate the interior of the shadow along the borders, thereby forming the penumbra. Even the interior of a shadow is normally not completely dark because light from the surroundings is scattered into the shadow region.

Suppose you hold the book over a pool of still water. Do you see a shadow? If you do, where is it? The answers depend on

several factors, including the depth of the water, its turbidity and what lies along the bottom. If the pool is shallow and clear and has a bottom such as concrete that does a not absorb all the light or reflect it like a mirror, you can see a shadow on the bottom. Usually, however, you do not see it in its true position.

Again the cause lies with the rays that pass the edges of the book and define the borders of the shadow. When the rays travel through the air-water interface, they are refracted because the effective speed of light in water is less than it is in air. If the sun is directly overhead, the rays remain vertical; otherwise they intersect the interface at an angle to the vertical and are refracted so that they are more nearly a vertical.

On reaching the bottom of the pool the rays are scattered in many directions. Some of the light moves upward and is refracted through the water-air interface. Unless the rays are vertical, the refraction increases their angle to the vertical. You extrapolate straight back along the rays and into the water without allowing for the refraction. The origins of the rays appear to be the points where the extrapolations intersect the bottom surface. Those points lie on the borders of the shadow because the intermediate region appears a to be dark. Since you do not allow for refraction, the shadow you see is usually displaced from the true shadow.

The amount of displacement depends on your angle of view. If you look directly down on the true shadow, the rays scattering from its borders travel vertically through the air-water interface with no change in direction. Your extrapolation of them into the water goes to the true position of the shadow. With any other angle of view you miss the true shadow.

If the bottom completely absorbs the light, the shadow is invisible. Can you see it if the bottom reflects like an ideal mirror and the sun is the only source of light? Yes, provided you position yourself to intercept the reflected rays. From all other angles of view the illuminated regions of the bottom are as dark as the shadow.

A shadow at the bottom of a pool of water is not completely dark because the sun adds a penumbra to it and light from the surroundings is scattered out of it. In addition some direct sunlight is scattered from the bottom, reflected from the water-air interface and then scattered to you from within the shadow region. A still brighter light is scattered from the surroundings, including the sky, and then is reflected from the top of the water. Some of it reaches you along the route taken by the rays from the borders of the shadow. The composite scene is a shadow overlain by faint reflected images. The scene is puzzling because the reflected images may appear to be distant whereas the shadow seems to be on the bottom of the pool.

To check this observation I sat by a shallow puddle of water on a sidewalk. The sun was behind me and a building

silhouetted against the sky was in front of me. Within my shadow on the puddle I saw reflections of the building and the sky. The apparent distance to the building equaled the true distance between the building and the puddle. I seemed to be looking through a hole at the bottom of the puddle. The image of the building's concrete walls was dim. The images of the windows were brighter because the windows scattered more light than the walls. The image of the sky was even brighter. I could see my reflection if I looked almost directly down on the water. Light from the surroundings was scattered from my face and then was reflected from the air-water interface. Faint colors were also visible.

Deep pools of clear water often display indistinct shadows. The penumbra is broader, decreasing the visibility of the shadow, and there is more opportunity for light to be scattered to you from within the shadow region.

The appearance and the position of your shadow in a pool change markedly if the water is turbid. The light is scattered from the suspended particles. If the concentration of particles is moderate and the water is not too deep, light may still reach you by being scattered from the bottom. Your shadow is visible but its edges are muddled because the scattering does not take place in a single plane. The interior of the shadow is brightened by light being scattered from the shadow region. With more turbidity the amount of light reaching the bottom is insufficient for you to see a shadow there. Instead you see light that is scattered from the suspended material near the surface of the pool. Your shadow then seems to lie near the surface, probably again with muddled borders.

In The Nature of Light & Color in the Open Air Marcel Minnaert argues that in some conditions of turbidity you may not be able to see the shadow of someone standing farther along the edge of the pool. If the pool is so turbid that it is almost the consistency of mud, the light is scattered from the upper surface with little penetration. Your shadow and the shadows of other objects appear on the surface in their true positions. Because the scattering takes place in what is almost a single plane, the shadows have sharp borders.

The surrounding sunlit mud is darker than dry dirt would be. Why is wet dirt darker than dry dirt? Craig F. Bohren of Pennsylvania State University recently explained the phenomenon. When the particles are surrounded by water instead of air, their scattering of light shifts forward, that is, downward into the bed. The reason is that water more closely matches the index of refraction of the particles than air does. With the shift in scattering direction the light is scattered many more times from wet particles than it is from particles surrounded by air. At each scattering point some of the light is absorbed. Hence the light that is scattered in your direction is dimmer than it would be in dry dirt.

Reflections in puddles are often distorted even when the water is still. Examine a puddle nested in a small "step" formed by

two uneven concrete slabs. The flat section of the puddle reflects the surroundings as a mirror would, but the part next to the step yields distorted reflections. The surface there is curved because of the molecular attraction between the water and the concrete along the side of the step. Similar distortions are caused by the curved surfaces surrounding leaves and other objects that float in a puddle. If a pencil is inserted vertically into a puddle, the water is pulled up along its shaft. The sudden change in the reflected images creates the illusion that the pencil pulls images toward it. Actually the curved water surface reflects images to you from objects farther to one side of you than the flat water surface did.

In 1953 Stephen F. Jacobs of the University of Arizona noted a curious pattern that can be seen when breezes blow over a pool of moderately turbid water at least a meter deep. Stand somewhat above the water and look at it near the shadow of your head. Flickering bright streaks seem to radiate from the shadow. They may create the illusion that the entire pattern rotates about your head.

The streaks are due to breeze-driven waves. In a calm, sunlight enters the unshadowed areas of water. The light is scattered from the suspended particles, and you see a uniformly bright pool. If breezes play over the pool, the variations in the shape of the surface alter the refraction of light into and out of the water. You no longer receive scattered light from the entire sunlit part of the pool. Jacobs believes the only regions that still send scattered light to you are those where the water is momentarily flat. I think some of the curved regions also contribute. In any case the water is bright in only a few places at any given instant.

Why do the bright spots appear as radial streaks? Each streak is similar to a narrow shaft of light penetrating a dark, dusty room. What you see is light scattered from the dust particles, but what you perceive is a beam crossing the room.

The radial orientation of the streaks in water is an illusion. Suppose you were to look along the length of an array of long,

parallel rods [see illustration at left below]. The scene offers at least two cues about depth. The outer ends of the rods seem to be near because their faces are visible. The tapering of the rods also reveals depth. Without the cues you might see the figure as a flat array of rods aligned along radial lines from the center of your perspective. You make a similar interpretation of the streaks in the water. Lacking cues about depth, you conclude that they are on the surface and that they point toward the position of the eyes in the shadow of your head.

A coloring that can appear in clear water was discovered by Frank S. Crawford, Jr., of the University of California at Berkeley while he was relaxing in a hot tub. The water was dappled with sunbeams streaming through the leaves of a tree. A companion noticed that the spots of light formed by the sunbeams on the bottom of the tub were either completely white or had colored edges, depending on how they were viewed. If you sit with the sunbeams passing over a shoulder, they are white. If you sit facing the sun, the near edge of a spot is red and the far edge is blue.

The colors are due to the spread of the color components in the initial white sunlight as it is refracted into the water. The blue changes its direction of travel at the interface more than the red does, the intermediate colors green and yellow change directions by intermediate amounts. Because of the spread, the red light and the blue light are scattered from the bottom at different points.

If you sit with your back to the sun, the only rays that return to you from the bottom are those that travel almost in reverse along the initial path of the light. A ray of each color travels back to you in this way, passing through the same point on the water-air interface. You perceive the combination of colors as being white. The source of the light appears to be a single spot on the bottom. The spot is displaced from the true scattering points for the colors because you do not allow for the refraction of light at the water-air interface.

If you sit facing the sun, the rays of various colors are scattered from the bottom and pass through the interface at

different points. You perceive them as originating at different but overlapping spots on the bottom. The center of the overlap is white, but the far edge is blue and the near edge is red Recently Thomas Gold of Cornell University rediscovered a puzzling property of a body of water covered with waves. Photographing the reflection of a ship's mast, he found the expected sinuous image. He also saw, off to one side of the image, an isolated loop that was an image of a short section of the mast. The image within the loop was the sky on the far side of the mast, and the image outside the loop was the sky on the near side of the mast. What happened was that while Gold was making the exposure a small region of the water surface tilted and curved in such a way as to reflect the section of mast. Provided the water surface has no sharp waves and no area of it is hidden from view by waves, such isolated reflections of a mast must form complete loops.

To understand the loop's formation, label the points on the section of mast and their corresponding points in the loop. Call the highest point A and its reflection A'. The next-lower point on the section, B, is reflected twice in the loop, once on each side of A'. Call the lowest point on the section Z and its reflection Z'. The next-higher point on the section, Y, has two reflections, one on each side of Z'. All the points between A and Z have two reflections in the loop. Thus the section is imaged as a closed loop.

David K. Lynch of the Aerospace Corporation Space Science Laboratory in Los Angeles elaborated on Gold's observations by noting that a pool of water covered with waves can also display "land pools" and "sky pools." These images are small, isolated patches that reflect extended sources of light such as mountains. A point source of light can also create an extended image. If it is photographed with a slow shutter speed, the image is sinuous and probably overlapping because the waves move during the long exposure. If the shutter speed is fast, the image is a short line, with ends corresponding to the opening and closing of the shutter. You might like to study further the different types of reflected images that can be photographed in these circumstances.

Bibliography

THE NATURE OF LIGHT & COLOR IN THE OPEN A. R. M. Minnaert. Dover Publications, Inc., 1954.

REFLECTIONS ON CLOSED LOOPS. David K. Lynch in Nature, Vol. 316, No. 6025, pages 216-217; July 18,1985.

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