Academic journal article The Science Teacher

The Physics of Rainbows

Academic journal article The Science Teacher

The Physics of Rainbows

Article excerpt

There is no physical rainbow in the sky. The colorful bow that has fascinated us for eons does not have an independent existence; rather, it's a spectrum of colors that converge in the mind of the beholder (or photosensitive surface of a camera). It is seen when the early morning or late afternoon Sun illuminates a region of the sky that's permeated with water drops. Each drop acts as a spherical prism that refracts sunlight, internally reflects it, and refracts it a second time to disperse the components of sunlight into the solar spectrum. To better understand rainbows, consider white light incident on a glass prism (Figure 1).

Dispersion of light in a prism

When a beam of white light first encounters the surface of a glass prism, it loses speed and bends from its straight-line path. We say it refracts into the glass, separating into its component colors, or frequencies. The speeds of different frequencies of light in transparent media vary, with light of high frequencies being slowed more than light of lower frequencies. The red part of the white beam slows and bends as it enters the glass, but slower-moving violet bends more. All the component colors of white light separate in the glass, though only red and violet are shown in Figure 1. When emerging, light undergoes a second refraction, and the separation is further increased. The separation of light into colors arranged according to frequency is called dispersion.

Dispersion in water

Dispersion also occurs in water, where violet light is slower than red light by nearly one percent. Figure 2 shows a two-dimensional view of dispersion in a water drop. Follow the ray of sunlight as it enters the drop. Some light is reflected (not shown), and the remaining light refracts into the water where it is dispersed into its spectrum colors, red being deviated the least and violet the most. Upon reaching the opposite side of the drop, each color is partly refracted out into the air (not shown) and partly reflected back into the water. Arriving at the lower surface of the drop, each color is again partly reflected (not shown) and partly refracted back into the air. Refraction at this second surface, like that in a prism, increases the dispersion already produced at the first surface.

Dispersion and the rainbow

Although each water drop disperses a full spectrum of colors, an observer of a rainbow is in a position to see the concentrated light of only a single color from any single drop (Figure 3). If red light from a particular drop reaches the eye of an observer, violet light from the same drop reaches elsewhere. To see violet light, one must look to a different drop lower in the sky. This explains why the top of a primary rainbow is red, and the bottom is violet. In-between angles show orange, yellow, green, and blue. Many millions of drops produce the whole spectrum of visible light.

The bow shape of the rainbow

The bow shape of a rainbow is a consequence of spectral colors emerging at specific angles. Each rainbow color relates to a characteristic angle of dispersion. The color red, as we've seen, always disperses at 42.4[degrees] to beams of sunlight. The drafting triangle in Figure 4 has fixed angles. When the triangle is rotated along the dashed line, it sweeps out a semicircular arc. An eye at the vertex sees same-angle locations along the dashed line. …

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