Why does a rainbow always curve into the same arc?

It's never a straight stripe or a square. Why does a sky full of separate raindrops make one curved band of colors? Let's start with one drop, then investigate a whole sky.

1What a raindrop does to sunlight

White light hides colors — and a drop splits them out

You only need two ideas. Watch each one:

White light is colors stacked up

Sunlight looks white, but it's really every color bundled together. Bend it and the colors fan apart, because each color bends by a slightly different amount.

A raindrop is a tiny mirror-ball

Light dives into a round drop, bounces off the back, and comes back out. On the way in and out it bends — so it leaves as a little fan of split colors.

2Two paths light can take

Straight-through light vs the bounce-back ray

Light hits a drop and can go two ways. Only one of them builds a rainbow:

Straight-through

Just passes through

Light that passes through without an internal reflection does not form the primary rainbow seen opposite the Sun.

Bounce-back ray

Bounces off the back

Light that bounces once off the back leaves the drop fanned into colors — with many of the rays clustered near a special angle.

3Your turn — aim a sunbeam at one drop

Slide where the light hits and watch the colors come out

Move the sunbeam up and down across a single drop. Watch it dive in, bounce off the back, and leave as split colors. The exit angle changes as you slide — but aim near the edge and the colors crowd together and pile up toward one special angle (about 42°). That bunching is exactly why the bow glows brightest there.

colors leave at about 42° out from your shadow (the point opposite the sun)
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4Now fill the sky with drops

A new viewpoint: which drops will send you color?

Keep the Sun and the field of drops fixed. Now take a step sideways. Use what you found about the angles from one drop to predict what a new viewpoint will change.

Guess before you take a step

When you step sideways, will exactly the same drops still send the bright rainbow colors to your eye, or will a different set light up?