The colors of the rainbow are a familiar sight to everyone, raising spirits and exciting feelings of well-being. Although often seen, the rainbow is seldom observed. A closer acquaintance increases the delights of the experience, as the full variety and extent of the display is recognized and appreciated.
The rainbow can be observed naturally in the rain falling from a thundershower, or artificially in the spray from a hose. In either case the sun must be shining (though the rainbow would be seen in artificial light as well) and not too high in the sky. Rainbows can be seen in the west in the morning, and in the east in the afternoon. Because thunderstorms are mostly an afternoon happening, rainbows are usually seen in the east under a storm that has drifted eastwards on the west wind. Thunderstorms are associated with rainbows because they are limited in area, and the sun shines between them. With continuous frontal rain, the sun is usually not visible, so there is no rainbow. Rainbows are made much easier to observe because they are opposite the sun, and the eye does not have to look into the glare.
The variables influencing the rainbow are the altitude of the sun, and the size of the raindrops in which the rainbow is seen. The rainbow is a cone making an angle of 42° with the antisolar direction, which is normally beneath the horizon for an observer on the surface. When the sun is at an elevation of 42°, only a little arc at the top is visible at the horizon. As the sun sinks, the arc of the rainbow rises in the sky, until at sunset it forms a semicircle. The eye interprets the light arriving on the cone as a circle somewhere in space, though the rainbow is really only a direction. If the observer is at a slight elevation, some of the rainbow can be seen beneath the horizon, in front of not too distant objects, which gives the impression of a physical existence not too far away. The story of the "pot of gold" at the end of the rainbow takes advantage of this illusion to send fools on a quest. The rainbow just keeps receding as they try to approach it. We should realize that the rainbow is a cooperative effect of many raindrops, with considerable depth, and that our visual impression is the best the visual sense can do with its data. When you see a rainbow, try to estimate its apparent distance from you, or its apparent size.
The figure at the right is a guide to the principal rainbow phenomena. The primary bow at 42° is only a part of the whole, but the brightest part. Impure spectral colors vary from red on the outside to blue (violet) on the inside, provided the incident light is white. The actual colors depend on the size of the raindrops and the constitution of the incident light. Outside the primary bow is the secondary bow at 51°, with the order of colors reversed. This bow is fainter than the primary bow, but is nearly always there with close observation. Between the two bows is a dark annular region, Alexander's Dark Space, where scattered light from the raindrops is a minimum. Inside the primary bow, and outside the secondary bow, are supernumerary bows of quite variable appearance and color. Usually several are visible inside the primary bow, colored alternately pink and green. The supernumerary bows outside the secondary bow are often too faint to be seen.
The colors in the rainbow are impure spectral colors, and depend on the size of the drop. A normal primary rainbow from large raindrops (greater than 1 mm diameter) contains easily distinguishable bands of green, yellow, orange and red, with very little blue, although violet does appear. There are almost always numerous supernumerary bows directly adjoining the violet. The red disappears for smaller drops, and is gone for 0.2 mm drops. Even smaller drops give a pale, broad bow with prominent violet, and separated supernumerary bows. Whiteness appears for drops less than 0.1 mm in diameter. The mist-bow occurs for drops less than 50 μm in diameter, typical cloud droplets.
If you examine the rainbow through a Nicol prism or a good Polaroid screen, such as a sunglass lens, the light of the primary bow will be found to be almost completely polarized. The direction of polarization is radial, from the antisolar direction. The secondary rainbow is also highly polarized, but not quite as much as the primary bow. The polarization shows conclusively that the rainbow is a result of refraction.
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