San José State University

applet-magic.com
Thayer Watkins
Silicon Valley
& TornadoAlley
USA

The Order of Colors
in a Rainbow

Primary Rainbows

In a primary rainbow a ray of light enters a rain droplet and is reflected once. It leaves the rain droplet with its direction shifted from a direct reflection by 42° for red light and 40° for blue light. In the spectrum of light coming from a particular water droplet the blue is on top and red is on the bottom. If the ray of red light enters the pupil of the observer then the ray of blue from the same rain droplet is too high and misses the observer's eye. But there is another rain droplet a little farther away for which the blue ray does enter the eye of the observer. The red from this rain droplet is too low and misses the observer's eye. The blue light that does enter the observer's eye has a smaller elevation angle than does the red light that enters the observer's eye. Therefore the combination of red light from the nearer droplet and the blue light from the farther droplet has the red color above the blue color.

Shorter wavelength blue light is refracted more than longer wavelength red light. In the case of the single internal reflection for a primary rainbow the light rays are approaching the 180° for a total reflection, but they fall short of it. Because of the greater refraction of blue light it falls short of the 180° by less, 40°, than does red light with its 42° deviation. In the case of the two internal reflections for a secondary rainbows the rays have exceeded the 180° of total reflection and have gone beyond it by about 51°. Since blue is refracted more than red light it has gone beyond 180; by more, 53°, than red light with its 50° deviation from 180°. Thus, in contrast to the case for a primary rainbow, the blue is at the bottom of the spectrum from a particular raindrop.

As with the primary rainbow the different colors come from different raindrops.


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