Why does a rainbow always curve into the same arc?

It's never a straight stripe, never a square — always the same gentle curve. And try to run to where it touches the ground… it keeps sliding away. So what shape is a rainbow really, and where does it live?

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 shoots straight out the far side scatters every which way — no special angle, no rainbow.

Bounce-back ray

Bounces off the back

Light that bounces once off the back leaves the drop fanned into colors — and always near one 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

One rule makes a curve. The other makes a smear. 🌧️

Here's the whole rainy sky, and there's you, with your shadow on the ground. Each drop could send its colors to your eye. The big question is the rule: can a drop aim color at you from any angle, or only from one fixed angle? Guess first — then flip the rule and watch.

Guess before you flip the rule

Which rule makes a sharp curved rainbow instead of a smeared glow?