I have a longer answer on this from a couple of days ago..
Rainbows form by the refraction of sunlight in raindrops. The angle between the incoming sunlight and the refracted rays is between 40 and 42 degrees (so we see the rainbow in front of us, when the sun is low, and behind us. We see the colours because refraction of light waves affects different wavelengths of light (blue.. to red) slightly differently.
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