Rainbow in a Raindrop
Drag the sunbeam up and down the raindrop and see where its colors come out.
Bend, bounce, bend: the light bends going into the drop, bounces off its back, and bends again coming out, at less than 42°. Light like this makes the sky inside a rainbow a little brighter, but its colors overlap, so it looks whitish.
- Hits the drop
- 70% up
- Red comes back at
- 38.1°
- Violet comes back at
- 36.9°
- The colors spread over
- 1.2°
What’s happening
A raindrop is a tiny ball of water, and it works like a round prism. Sunlight bends as it goes into the drop, bounces off the inside of its back, and bends again as it comes out, heading back towards the sun. Water bends violet light a little more than red, so the colors come out going slightly different ways. However a sunbeam hits the drop, it never comes back wider than about 42°, and lots of sunbeams come back at almost exactly that angle, so the light piles up there. With the sun behind you, every drop 42° away from the shadow of your head sends you its brightest light: together they make a circle of colors, the rainbow.
Try this
- Move the sunbeam slowly from the middle to the edge. Where does the light come back widest?
- Pick many sunbeams. Where do the red lines bunch up?
- Which color comes back at the bigger angle, red or violet? So which is on the outside of a rainbow?
- Pick two bounces. Which way round are the colors now?
- On a sunny morning or afternoon, stand with your back to the sun and spray a fine mist from a hose. Where does the rainbow appear?
Learn more: why 42°, the second rainbow, and who worked it out
Why a rainbow is a circle. Each drop sends its brightest light back at 42° from the line running from the sun through your head to its shadow. The drops that lie 42° from that line make a circle round your shadow’s head, and that is where you see the rainbow. Usually the ground cuts the circle off, so you see an arc; from a plane you can sometimes see the whole ring. Red comes back at a slightly bigger angle than violet, so red is on the outside. Everyone sees their own rainbow, made by their own drops.
Why the light piles up at 42°. Going into the drop at an angle from the normal, the light bends to an angle , by Snell’s law, with about 1.33 for water:
Following it through one bounce and out again, it comes back at an angle from the way to the sun:
As the sunbeam moves from the middle of the drop to the edge, grows, stops, and shrinks again. Where it stops, a whole range of sunbeams come back at almost the same angle, so that is where the light is brightest: the rainbow. For bounces it stops where
With one bounce that is about 86% of the way from the drop’s middle to its edge. René Descartes worked this out in 1637 by following thousands of rays through a drop by hand; Isaac Newton later showed that the colors come from violet bending more than red.
The second rainbow. Some light bounces twice before getting out. It comes back at
which is never less than about 51°. So a second, bigger rainbow sometimes shows outside the first, with its colors the other way round (red on the inside). It is fainter, because at every bounce most of the light escapes through the drop’s back. Between the two rainbows no light comes back from either bounce, so the sky there is darker: it is called Alexander’s dark band, after Alexander of Aphrodisias, who described it about 1,800 years ago.
- Hoses and waterfalls: fine spray makes rainbows whenever the sun is behind you and low enough.
- Fogbows: in fog the drops are so tiny that the colors smear together into a wide, almost white bow.
- Faint extra bands: just inside a bright rainbow you can sometimes see thin pink and green stripes. Light is a wave, and waves through the drop add up and cancel out, which rays alone can’t explain.
- No rainbows at noon: when the sun is more than 42° up, the rainbow’s circle is entirely below the horizon. That is why rainbows show in the morning and late afternoon.