The light goes through the rain drop which acts like a prism and splits the light into different colours! Have a look at the picture in the link below. The light splits because each colour has a different ‘wavelength’ which means basically that they will reflect off of a surface differently, this is how they split.
Fun fact, the infrared region of light was found by a guy who measured the temperature of these colours created by putting sunlight through a prism, he noticed that the area with no (visible) light just past the red was the warmest and concluded that there must be light there that we cannot see, cool eh!
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