Why does a rainbow have exactly seven colors?

Short answer: it doesn't, really — and the number seven has almost nothing to do with physics.

When Isaac Newton first split sunlight with a prism in the 1660s, he only identified five colors: red, yellow, green, blue, and violet. Ten years later, he added two more — orange and indigo — specifically to match the seven notes of a musical scale, because he believed color harmony should mirror musical harmony. There was no experimental reason for this; it was an idea he imposed on the spectrum by analogy.

Physically, a rainbow is a continuous spectrum with no real boundaries between colors. The "seven bands" we're taught to see are a cultural convention, not a property of light. Most people, in fact, can't reliably distinguish indigo from blue or violet when looking at an actual rainbow.

I wrote a more detailed breakdown here, including why the human eye's three cone types make six colors a more natural count than seven: [rainbow Article]