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Light & Colour · Question 03 of 20

How rainbows form

Every rainbow is millions of raindrops each doing the same three-step trick with sunlight — and it only works from where you stand.

Plate VII — A raindrop, ray-traced refract · reflect · refract · 42°
Slide the sunbeam up and down the drop — the exit angle keeps stalling near 42°.
sunlightone bounce inside · each colour bends its own amount
FIG. VII — A RAINDROP, RAY-TRACED
Where the ray enters the drop 82% from centre
Slide it — the exit angle stalls near 42°. That pile-up is the rainbow.
Red exits at
42.0°
Violet exits at
40.4°
The drop bends the light going in, bounces it off the back wall, and bends it again going out. Each colour bends a tiny bit differently, so white sunlight leaves as a fan of colours. Try every entry height: the exit angle keeps landing near 42° — that's why the whole sky's drops agree on one arc.
The short answer

Every raindrop is a tiny round window that bends sunlight and fans it into colours. Millions of drops together paint an arc — but only when the sun is behind you.

What's actually happening

A raindrop is a tiny glass bead. Sunlight entering it bends (refraction), bounces once off the back wall (reflection), and bends again on the way out. The bending is what splits the colours: red bends a little less, violet a little more, so each drop fans white sunlight into a tiny spread of colour.

The trick is in the angle. The geometry of a sphere concentrates the exiting light at very nearly one angle — about 42° from the direction of the incoming sunlight for red, 40° for violet. So each drop flashes you exactly one colour, decided by where it sits relative to your eye and the sun. Millions of drops at the 42° ring flash red, drops slightly inside that ring flash orange, and so on down to violet. The "bow" is just that set of rings, drawn in falling water.

Which means a rainbow is not a thing in the sky — it is a relationship between the sun, the rain, and you. Step sideways and your rainbow moves with you; the person beside you sees light from a completely different set of drops. Nobody has ever stood at the end of a rainbow because the end retreats exactly as fast as you walk toward it.

Try it at home Grow your own rainbow
  1. 1Pick a sunny late afternoon — a low sun makes a taller bow.
  2. 2Stand with your back to the sun and spray a fine mist from a hose or spray bottle in front of you.
  3. 3Look about 42° away from your own head's shadow. Move the spray until the arc appears — then take one big step sideways and watch the whole rainbow move with you.