READING ELIZABETH WOOD'S SCIENCE from Your Airplane Window is a sure cure for the boredom of air travel (unless, of course, you end up in that terrible row of interior seats). The book is a rich collection of experiments and observations for an airplane passenger. Over the years I have replicated many of Wood's demonstrations and have also scribbled notes about new ones in the margins of her book. This month I explore some of the results.

In particular, an airplane window offers several lessons in optics. The window usually consists of three layers. The outer two are closely spaced and are sealed to the window frame to maintain a comfortable air pressure within the cabin when the airplane flies at high altitude; the third layer protects the sealed layers.

If you are sitting on the shady side of the aircraft, the window may look clear and unblemished, but on the sunny side you may find that the outermost layer is covered with tiny bright scratches. They are visible on that side of the plane because they scatter sunlight to your eyes. Most of the scratches were engraved by rough particles that swept over the window.

You see only a fraction of the total number of scratches on a window; other, imperceptible ones are not oriented in such a way as to scatter light to your eyes. If you move your head and change your angle of view, or if the airplane's course changes, you may see a different set of scratches or they may all disappear.

Wood pointed out that the bright scratches form patterns. If you look toward the sun, the bright scratches appear to lie on short sections of concentric circles around the sun. If instead you sit so that the cabin wall blocks your view of the sun, they may appear to lie on straight, parallel lines.

Two features of the scratches puzzled me. When a window is bathed with sunlight, why are only some of the scratches

brightly lighted? And why, in the case of those few, is the brightness limited to a small part of the full length of the scratch? After a few flights I figured out that when light scatters from a point along a scratch, it spreads out primarily in a flat fan whose plane is perpendicular to the length of the scratch [see illustration on the right]. I estimate that the angle of the fan is small, often less than 30 degrees; the light spreads less than 15 degrees to each side of the scratch. The spread of light out of the plane of the fan is much smaller-something like one degree. Therefore if I see a bright point 11 in the window, my eyes must be in the plane of the fan of light scattered from that point, or within a degree of the plane. The rest of the scratch certainly scatters sunlight, but the light misses my eyes, and so the rest of f, the scratch is imperceptible-as are all the scratches that send no light whatsoever in my direction.

Suppose the sun is directly off to the side of the aircraft, so that the light rays are initially perpendicular to the window. Any bright scratches to the left and right of the sun are vertical and emit horizontal fans of light that reach your eyes. Bright scratches above and below the sun are horizontal and emit vertical fans of light that also reach you. In addition there are bright scratches at intermediate positions around the sun that happen f, to be oriented so that they send a G fan toward you. Many of the bright scratches lie within 15 degrees of the sun; only a few lie farther out. The density of bright scratches is high close to the sun, because the fans of scattered light are not exactly flat and you receive light from scratches of any orientation.

The 15-degree "limit" determines 15 how much of the window has bright scratches. If you sit far from the window, its edges may be within the limit and the entire window will be covered with bright scratches. If you sit next to the window, some of it may be beyond the limit, so that only part of it will have visible scratches. The visibility of scratches also depends on how high the sun is and on the course of the aircraft. For example, if the sun is high, most of the light may be scattered to the floor rather than to you, and the window will appear to be free of scratches.

The arrangement of bright scratches on concentric circles or parallel lines is an illusion. Your brain automatically seeks to impose order on the random pattern of bright spots on the window; provided there are enough bright spots, it brings up to consciousness an illusion that the spots form a geometric pattern. If there are too few bright spots, the illusion disappears and you see the spots as they are randomly scattered.

When there are abundant bright scratches, I often see long streaks of light that seem to point toward the sun. On close inspection I discovered that the streaks are fans of light, from adjacent scratches, that overlap. A close view also revealed that the bright region on a scratch is normally a narrow oval. The short axis of the oval is set by how much of the fan of light is intercepted by the pupils of my eyes. The long axis of the oval is set by the actual shape of the scratch (it may not be straight) and by the fact that rays from the sun are not perfectly parallel but spread by half a degree (because that is the angle the disk of the sun occupies in our field of view). The edges of the oval are often colorful, indicating that the scattering separates the colors in the white sunlight much as a laboratory diffraction grating does.

On a recent flight I spotted another curious optical effect. I was seated on the sunny side of the plane near the front edge of the wing. A jet engine suspended about halfway out on the wing extended forward, beyond the leading edge. Sunlight was reflected from the fuselage to the engine and thence back to me, so that I could see a mirrorlike image of the fuselage on the engine. The outline of the fuselage was distinct in the image, but the row of windows formed a dark band, because the windows reflected sunlight to the engine only weakly. I wondered where I was in the image. Even when I pressed my face up against the window, I reflected too little light to be perceptible. I needed a brighter reflector. I unstrapped my watch and turned its metallic back toward the sun. After I had played with the orientation of the watch for a few minutes, a bright spot appeared in the dark band along the engine: I had found myself.

You can also have fun with reflections when you are flying at night, provided you sit next to a window. Turn on the overhead light so that you and the objects around you are illuminated. If you face directly into the window, you will see an image of your face. The edges of the image are fuzzy, because you are actually seeing a composite of three images-one of them from each of the three layers in the window. The image reflected by each layer is as far from the layer as your face is. The farthest layer produces an image that is slightly smaller in your field of view than the image reflected by the closest layer, and the overlap of images yields the fuzzy edges.

Hold a shiny object such as a metal pen out toward the seat in front of you and then look at the window. You will probably see three images of the pen. If you look at the window obliquely rather than directly, you separate the images reflected from each layer. If the view is slanted enough, you will find that each of the three images actually consists of a pair of overlapping images. In each pair the nearer image is a reflection from the front (the near side) of a layer and the farther image is a reflection from the back (the far side) of the layer.

The reflections giving rise to the various images are indicated in the illustration at the left below. Each reflected ray is mentally extrapolated backward, so that it appears to have originated beyond the window. (For clarity the illustration has been simplified by assuming that the observer is far from the window; a single ray from the pen is responsible for the various reflections and images. Actually the observer is near the window and a slightly different ray from the pen is needed for each reflection; all the reflected rays converge at the observer's eyes. I shall ignore that detail here.)

The images are dim because every time the light reaches a surface (either the front or the back of a layer) only a small fraction of the light is reflected; the rest of it continues to travel outward. The dimness of the images makes them hard to make out during daylight, when a flood of light comes to your eyes from outside the plane.

If the night is dark and if the light reflecting off the pen toward the window is particularly bright while the cabin is otherwise dark, you may see even more images in the window. They are caused by multiple reflections between layers or even from the front and back surfaces of a single layer. For example, a ray from the pen can pass through the first layer and be reflected from the middle layer, be bounced back by the first layer and then reflected again from the middle layer before it reaches you [see Figure 4]. The bounced light creates another image of the pen, but this image is quite dim, because the three reflections leave a final ray of low intensity. You may notice other images in a window. Can you figure out how they develop from multiple reflections?

I can see images arising from multiple reflections better when the aircraft is waiting for takeoff at night. I switch off the overhead light and examine a runway lamp either ahead of me or to the rear. Trailing off to one side of my direct view of the runway lamp there are images that must have been generated by multiple reflections from the window layers or from the front and back surfaces of a single layer [see illustration above left]. A runway lamp that is directly off to the side of the aircraft does not give such a display. The light from it does undergo multiple reflections, but the resulting images overlap and cannot be distinguished. When the light from the lamp reaches the window along a slanted path, the images due to multiple reflections between layers are separated enough to be distinguished; the images due to multiple reflections within a single layer are more tightly spaced and are harder to distinguish.

The image that lies closest to the direct view of the lamp results from a double reflection between the outer two layers of the window. The light passes through the outermost layer, is reflected from the middle layer and then back to the outermost layer before being reflected to my eyes. The next side image is caused by light that is reflected once from the inner layer and then once from the middle layer. Near by, but slightly farther from the direct view of the lamp, is an image due to light that is reflected from the inner layer and then the outermost layer. Other images may also be present, but they are dimmer, because they involve four or more reflections from the layers. Their positions depend on both the angle at which you peer into the window and the angle at which the lamp's light reaches the window.

On a night flight recently I was seated on the right side of the plane in an oddly configured row where there was extra space between the window and my window seat. The space allowed me to peer back into the window just behind me. Before takeoff I sketched how the window yielded three images of an armrest of the seat behind mine. When I moved my head forward, the images maintained their relative spacing. Later, at high altitude, I again examined the reflections. This time their spacing was different. Also, when I moved my head forward, the outer two images moved in opposite directions: the outermost image unexpectedly moved forward and the middle one moved to the rear.

I suspected the reason for the different spacing of the images and their odd movements was that the sealed layers in the window were no longer flat, having flexed outward as the air pressure decreased outside the aircraft. After making a few sketches I understood the images. The outermost one came from light rays that happened to be reflected from just to the left of the center of the outermost layer. When I moved my head forward, I intercepted a different set of rays, which were reflected from farther to the left of center. If the layer had been flat, both sets of rays would have seemed to originate at the same place outside the window, and the image I perceived there would have been stationary. Because the layer was curved, however, the second set of rays appeared to originate to the left of the first set, and so when I moved, the image shifted to the left with me.

The middle image came from rays reflected from the middle layer. These rays were reflected from just to the right of the center of the layer. When I moved forward, I intercepted rays reflected from farther to the right of center, making the image shift to the right-in the direction opposite to that of the outermost image.

When the plane landed, I again studied the movement of the reflections when I moved my head forward. This time the outermost and innermost images maintained their relative spacing, indicating that the outermost layer was again flat. The middle image still moved in its peculiar way, though: apparently the middle layer of the window had not yet adjusted to the return to normal air pressure. On later night flights I found that the curvature of the layers could also be detected when I held a metal pen in front of me. When the reflections were near an edge of the outer layers, the images of the pen were curved.

If you fly on a sunny day and on the sunny side of the aircraft, watch the reflections of the sun from water surfaces below. The spectacle is best when the aircraft is at a low-to-moderate altitude and when there are no waves on ponds or lakes. A flat water surface is a mirror that reflects a bright image of the sun. If the body of water is large enough, the image occupies the same half-degree angle in your field of view as the sun would in a direct view; a pond that is large enough to reflect a complete image when the plane is low may give only a partial image at higher elevations.

When there are a number of water surfaces below you-ponds, canals or even swimming pools-the sun's image plays hide-and-seek, skipping between water surfaces but always constrained to stay along a path set by the flight of the aircraft; you may appear to be moving over scattered pieces of a shattered mirror. Other shiny surfaces, such as the slanted metal roof of a shed or, if you are low enough, the windows of cars in a parking lot, send up brief flashes of light, which may be well off the sun's path over flat water. Even the bumpers on the cars or the metal traffic signs along roadways enter into play. I was surprised by the reflections from signs, which would not appear to be oriented correctly to reflect the sun upward. Apparently the sun is so bright that even the top edge of a sign can contribute a noticeable albeit fleeting reflection.

Here is another reflection observation, which I shall leave for you to figure out. While flying on the sunny side of the aircraft with the sun above me, I noticed two rows of rectangles on the wing. Each rectangle was marked by a bright border. The rectangles in the farther row were longer than those in the nearer row. Once, when the pilot tilted the wing upward, the rows slid toward the fuselage and a third row appeared just beyond the second one. Obviously the rectangles were images of the windows. The puzzle is: Why were the images not in a single row?

Air travel provides some lessons in high-pressure physics as well as in optics. Although airliners have pressurized cabins, the cabin pressure is always less than the air pressure on the ground. One way to monitor the change in air pressure in flight is to examine one of those sealed, plastic containers of gelatinous salad dressing that are served with dinner. When the plane is on the ground, the flexible top of the container bulges inward, but when the aircraft is at high altitude, the top bulges out, because the cabin pressure is less than the air pressure inside the container.

If you shake the container to mix its contents, you coat the inside of the top of the container with salad dressing. When you then open the container by peeling off the top (if you can find the peelable edge), the sudden exposure of the interior to the low pressure in the cabin will blow the gooey coating outward. To avoid squirting salad dressing into your lap, take care to aim the opening toward the salad.

Bibliography

EFFECT OF ENVIRONMENTAL CHANGES ON THE GHOSTING OF DISTANT OBJECTS IN TWIN GLAZED WINDOWS. W. Swindell in Applied Optics, Vol. 11, No. 9, pages 2033-2036; September, 1972.

SCIENCE FROM YOUR AIRPLANE WINDOW. Elizabeth Wood. Dover Publications, Inc., 1975.

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