Physics

Why a rainbow is always a circle 42° around your shadow

30seconds
The 30-second version

Every rainbow is part of a circle centred on the shadow of your head, with its red edge about 42° away. That number comes from inside a single raindrop.

Sunlight bends as it enters a drop, bounces off the back and bends again on the way out. Rays leave at many angles, but none go wider than about 42°, and near that limit they pile up. The pile-up is the bow. Violet bends a little more than red, so it piles up slightly closer in, which puts red on the outside.

Light that bounces twice makes a fainter second bow with reversed colours, and the gap between them is a darker strip of sky.

Deep dive · 5 min
Deep dive · 5 min