How does a rainbow form?

The principle

A rainbow. You need two things: sunlight and falling rain (or spray). The colours don’t come from the sky or the clouds. They are made inside each single raindrop.

Step 1: Light bends into a drop. White sunlight hits a round raindrop. As it goes from air into water it slows down a little and changes direction: it bends. It is the same thing that makes a straw look bent where it goes into a glass of water.

Step 2: Colours split and bounce. White light is really all colours mixed. Each colour bends by a slightly different amount, so they fan out, just like light through a glass prism. The light then bounces off the back of the drop and comes out the front again, bending once more. Red comes out at about 42° from the direction the sunlight was going, violet at about 40°.

Step 3: The sun is behind you. Imagine a line from the sun, through your head, to a point in front of you (below the horizon when the sun is up). Every drop that sits about 42° from that point sends red light into your eye; drops at about 40° send violet. All drops at the same angle form a circle around that point, and that circle is the bow. The ground usually hides the bottom half; from a plane you can sometimes see a full circle.

Step 4: The sun must be low. The top of the bow is about 42° minus the sun’s height. With the sun about 15° up, the top of the bow is about 27° above the horizon. Once the sun is higher than about 42°, the whole bow is below the horizon and you can’t see it from the ground. That is why rainbows show up in the morning and late afternoon, not around noon in summer.

Step 5: A second, fainter bow. In some drops the light bounces twice before it leaves. That makes a second, fainter bow at about 51°, outside the first one, and the extra bounce flips the colours: red is on the inside. The sky between the two bows looks a bit darker.

Primary bow or secondary bow?

• Primary bow (about 42°): bright and easy to see, red on the outside, violet on the inside. Downside: only when the sun is low and behind you, with rain in front of you.
• Secondary bow (about 51°): a bonus bow higher up, colours flipped. Downside: much fainter, because some light is lost at each bounce, so it often isn’t visible at all.

Try it yourself: stand with the sun behind you and spray a fine mist from a garden hose. You’ll see your own little rainbow, at about the same 42° angle.