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A drop of water bends light, just like a magnifying glass (in fact you can make a simple magnifying glass just by capturing a drop of water in a small loop and looking through it). And the water bends blue light more than it bends red light.
For a rainbow to form, you need the Sun behind you and a rain shower in front of you. The sunlight is bent as it enters the front of each drop; then it gets reflected off the back of the drop, and bent again as it comes out. What colour you see depends on the angle between your eye and the drop and the Sun. If you think about that you will see why the rainbow is part of a circle.
In fact, from a plane you can sometimes see a full circle rainbow.
There are in fact several ways the light can bounce around inside the drop, so sometimes you can see two rainbows, the “normal” one and a smaller, fainter one inside it, with the order of colours reversed.
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