A rainbow is the result of refraction, which is the bending of a wave. In this case, it is the bending of a light wave. Sunlight is composed of all colors, but they mix together to give the Sun a more whitish appearance. The Sun emits more yellow/green light so it appears a bit more yellow, but there's also red and blue light emitted. When this light passes through water in the atmosphere, it bends. Since light of different wavelengths (colors) bends at different angles, the "white" light separates into colors, giving you a rainbow.
What you may not realize is that rainbows are actually circles. In almost all cases you see half of a circle, or part of the arc of the rainbow. If you can get high enough, say at the top of a mountain, or in an airplane, it is possible to see a full circle. Now you have something to look for on your next plane trip!
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