How Rainbows Form: Sunlight, Water Drops and Angles

A rainbow looks like an object hanging in the sky, but it is really an effect of light, water and where you happen to be standing. No two people see exactly the same rainbow, because each viewer sits at the point where the light reaches their eyes at the right angle. Understanding how it works turns a pretty sight into a neat piece of everyday physics.

Key takeaways

• A rainbow forms when sunlight enters raindrops, bends, reflects off the back and bends again on the way out.
• Different colours of light bend by slightly different amounts, which spreads white light into a spectrum.
• You need the Sun behind you and water drops in front of you.
• The arc is part of a circle centred on the point opposite the Sun from your eyes.
• A rainbow is not a physical object, so you cannot reach its end.

Light, refraction and colour

Sunlight looks white but is a mixture of colours. When light passes from air into water it slows down and changes direction, a process called refraction. Because each colour changes direction by a slightly different amount, the colours begin to spread apart. Violet light bends a little more than red light, which is why red ends up on the outside of the primary rainbow and violet on the inside.

What happens inside a raindrop

Each drop does three things in sequence. Light enters the front of the drop and refracts. It then reflects off the inside back surface. Finally it refracts again as it leaves the drop and travels toward your eyes. The result is that the light is sent back roughly toward the direction it came from, concentrated at angles of about 40 to 42 degrees from the line pointing directly away from the Sun. That narrow band of angles is why you see a distinct arc and not a wash of colour across the whole sky.

Why the rainbow is an arc

Imagine a line from the Sun through your head and onward to the point directly opposite the Sun, sometimes called the antisolar point. Raindrops that sit at the same angle from that line all send the same colour toward you, so they form a circle around it. From the ground you usually see only the upper part of that circle because the ground blocks the rest. From an aeroplane or a high viewpoint, you can sometimes see a full circular rainbow.

Double rainbows and other variations

Sometimes a fainter second rainbow appears above the main one. It comes from light reflecting twice inside each drop, which reverses the order of the colours so red is on the inside. The patch of sky between the two bows often looks darker. Rainbows can also appear in mist from waterfalls and garden sprinklers, since any cloud of small water drops can do the job when the Sun is behind you.

Why you cannot reach the end

Because a rainbow depends on your position, it moves when you move. As you walk toward it, the drops that form your rainbow change, and the bow appears to keep its distance. There is no pot of gold, and no physical place where the arc touches the ground.

Colours, angles and a smooth spectrum

The familiar list of red, orange, yellow, green, blue, indigo and violet is a convention, not a feature of the light itself. Sunlight spreads into a continuous band, and the number of named colours is a cultural choice. Isaac Newton, who famously split sunlight with a glass prism in the 1660s, settled on seven names partly because of an old fondness for that number. In a real rainbow your eye sees the colours blend into one another, and different people may pick out slightly different bands.

The angles involved are small but precise. Red light leaves the raindrops at about 42 degrees from the line pointing away from the Sun, and violet light at about 40 degrees. That two-degree spread is the whole width of the primary bow. Because the bow appears at a fixed angle from the antisolar point, its size in the sky does not depend on how far away the rain is.

Extra bands and polarised light

Look closely at a bright rainbow and you may see faint pink and green stripes just inside the violet edge. These are called supernumerary bows. They are produced by interference, the same wave effect that creates colours in a soap bubble, and they show that light behaves as a wave. They are most visible when the raindrops are small and similar in size.

Rainbow light is also strongly polarised, meaning its waves vibrate mostly in one direction. Polarising sunglasses can therefore make a rainbow look brighter or almost vanish as you tilt your head. Photographers use polarising filters for the same reason, to make a rainbow stand out or to tone it down.

How to see one on purpose

You need two things at once: sunlight behind you and water drops in front of you. Because the top of the bow sits about 42 degrees above the antisolar point, you can only see a rainbow from the ground when the Sun is lower than about 42 degrees above the horizon. That is why rainbows are common in the morning and late afternoon and rare around midday in the tropics and summer months.

You can make your own with a garden hose set to a fine mist, standing with the Sun behind you. Waterfalls and fountains work well on sunny days, and viewing from an aircraft or mountain can reveal the full circle.

A short history of understanding

Aristotle wrote about rainbows in the fourth century BCE, and scholars in the Islamic world made important advances. Ibn al-Haytham studied light and refraction around the year 1000, and in the early fourteenth century the Persian scientist Kamal al-Din al-Farisi explained the rainbow using a glass sphere filled with water as a model of a single drop. In 1637 René Descartes published a clear geometric analysis, and Newton later showed how white light splits into colours. Each step moved the explanation from myth toward measurement.

Frequently asked questions

Why are rainbows curved?

Raindrops at one particular angle from the antisolar point send the same colour to your eyes. Those drops form a circle, and you see the part above the horizon.

Can you see a rainbow at night?

Faint rainbows called moonbows can form when bright moonlight shines on water drops, but they are dim and often look whitish to the eye.

Why does red appear on the outside?

Red light bends slightly less than violet, so it leaves the drops at a larger angle from the antisolar point and appears on the outer edge of the primary bow.

Can a rainbow form without rain?

Yes. Any cloud of small water drops can do it, including spray from waterfalls, sprinklers and sea waves, as long as the Sun is behind you and shining on the drops.

Why is the sky darker between the two bows?

The area between a primary and a secondary rainbow is often darker because no light from the drops reaches your eye at those angles. This dark band is known as Alexander's dark band, after the Greek philosopher Alexander of Aphrodisias, who described it.

How long does a rainbow last?

It depends on the rain and the clouds. Often only a few minutes, because the shower moves on or the Sun is covered, but it can last much longer when conditions stay steady.

Sources and further reading

• Rainbow (Wikipedia)
• National Weather Service