Rainbows and the refraction of light

Light bends when it changes medium

Put a straw in a glass of water and it looks bent at the surface. Light slows down as it passes from air into water, and that change of speed bends its path. This is refraction. In water, light travels at about three quarters of its speed in a vacuum, and water's refractive index is about 1.33. A swimming pool looks shallower than it is for the same reason: looking straight down, it appears only about three quarters of its real depth. Water can be deeper than it looks, so in unfamiliar water do not judge depth by eye alone.

Each colour bends by a different amount

How much light bends depends slightly on its wavelength. In water or glass, short-wavelength violet and blue bend more, while long-wavelength red bends less. So when sunlight passes through a prism, each colour leaves at a different angle and the light spreads into a band from red to violet. Separating colours through differences in refraction is called dispersion. The scattering that makes the sky blue sends light off in all directions, whereas the refraction and dispersion that make a rainbow bend light in definite directions; that is the difference.

What happens inside a raindrop

A raindrop acts as a tiny spherical prism. Sunlight bends once as it enters the drop, reflects off the inside of the back surface, then bends again as it leaves into the air. Light that takes this route comes back out towards the side it entered from, the side where the Sun is, and it bunches up near a particular angle: about 42 degrees for red and about 40 for violet. So drops lying on a circle about 40 to 42 degrees from the point directly opposite the Sun each send one colour to your eye, and together they make a rainbow. That is why red is on the outside and violet on the inside.

• Bends once on the way in
• Reflects off the inside of the back
• Bends again on the way out
• Light bunches near 42 degrees for red, 40 for violet

When you can see a rainbow

The centre of a rainbow is always where the shadow of your head points, directly opposite the Sun. So to see one you must stand with the Sun behind you and raindrops in the sky ahead. That is why rainbows appear just after a shower when the Sun comes back out. When the Sun is high, the point opposite it sinks deep below the ground and the rainbow's circle hides below the horizon. The Sun must be lower than about 42 degrees for a rainbow to be visible from the ground, so mornings and late afternoons are better than midsummer middays. With the Sun behind you, a spray bottle or garden hose will make one for you.

Double rainbows and the dark band between

Sometimes a fainter second rainbow appears outside the first. This is light that has reflected twice inside the drops, and it forms near 51 degrees. The extra reflection flips the light, so the colour order is reversed: red on the inside, violet on the outside. Some light escapes at every reflection, so it is fainter than the first. The sky between the two bows is noticeably darker, because in that range of angles neither path sends light towards you. The sky inside the main rainbow is brighter than outside it for the same reason.

Everyone sees a different rainbow

A rainbow is not an object in one place but an arrangement of light visible only at a certain angle. Someone standing beside you sees light from slightly different drops, so strictly speaking everyone sees their own rainbow. Walk towards it and it moves away by the same amount, so you can never reach its end. A rainbow looks like a semicircle because the ground blocks the lower half of the circle; from an aircraft or a high mountain with a clear view below, you can sometimes see the full circle.

Seven colours is a convention

Calling the rainbow seven colours is closer to a human convention than a fact of nature. A real rainbow runs continuously from red to violet with no boundaries. The seven-colour division owes a lot to Newton, who split sunlight with a prism in the 17th century and grouped the colours into seven to match the musical scale. Some cultures and languages describe the rainbow as five or six colours. How many colours you see also depends on your eyes and on the size of the drops that day.

Common misconceptions and cautions

Rainbows are as misunderstood as they are beautiful. Knowing the following will help you find them. Don't end up looking straight at the Sun while scanning the sky for one, and when driving, don't let a rainbow hold your attention for long.

• A rainbow is an object in one place: its position depends on the viewer
• A rainbow can appear anywhere it's raining: only opposite the Sun
• The seven colours are sharply divided: the colours are continuous