ELI5 Rainbows - how are rainbows formed, and why is the color brown missing?

How are rainbows formed? How about double rainbows? Are rainbows really circles? Why isn't brown on the rainbow?

... We explain like i'm five!

Thank you to the r/explainlikeimfive community as always and in particular the following users whose questions and comments formed the basis of this discussion: intangible-tangerine, lastsasquatch, zanelightning, sirherald, dammitcaesar, larae_is_bored & jollyrogerninja

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