How are rainbows formed? The short answer
A rainbow forms when sunlight shines into millions of falling raindrops while the Sun is behind you.1 In each drop the light bends as it goes in, bounces off the back of the drop, and bends again as it comes out.13 Each colour bends by a slightly different amount, so white sunlight fans out into its colours.4 Raindrops about 42° from the point opposite the Sun send you red light, and drops at about 40° send you violet.58 All of those drops together draw the coloured arc you see.
In one sentence: a rainbow is sunlight, bent, bounced and split by raindrops, and sent to your eyes at about 42 degrees.
What you need to see a rainbow
Every rainbow needs three things:1811
- Sunlight, shining from behind you. You always look away from the Sun to see a rainbow.
- Water drops floating in the air in front of you: rain, spray from a waterfall, or mist from a garden sprinkler.
- A low Sun. The Sun has to be no more than about 42° above the horizon.311
That's why rainbows often show up in the late afternoon, as a shower moves away and the Sun comes out behind you.6 A quick test: if you can see the shadow of your own head during a shower, you're facing the right way.6
What happens inside a raindrop
Follow one ray of sunlight into one round raindrop:137
- Refraction in. Light travels more slowly in water than in air, so the ray bends as it enters the drop.
- Reflection. It crosses the drop and bounces off the inside of the back surface, like a curved mirror.
- Refraction out. It bends again as it leaves the drop and heads back towards the Sun's side of the sky, where you are standing.
Rays that hit different parts of the drop come out at different angles. But rays pile up near one angle, the angle where the light is turned back least. Scientists call this path the rainbow ray. So a drop sends out a concentrated, bright beam that you see about 42° from the point directly opposite the Sun.310 The French scientist René Descartes worked out this 42° concentration using the laws of optics.5 In the interactive, drag the sunbeam up and down the drop and watch the exit angle stop growing and turn back near 42°.
A giant raindrop in a dark room
About 700 years ago, the Persian scientist Kamal al-Din al-Farisi (1267–1319) couldn't study tiny raindrops, so he built a giant one. He filled a large glass globe with water and shone light through it inside a darkened room (a camera obscura). His experiments showed that drops split white light into the colours of the rainbow. Theodoric of Freiberg, in Germany, did similar experiments at the same time.4
What causes the colours: dispersion
Sunlight looks white, but it's a mix of many colours (wavelengths).1 Water bends each wavelength by a slightly different amount. Violet, the shortest wavelength, bends the most and red, the longest, bends the least.15 This spreading is called dispersion. The bounce off the back of the drop doesn't separate colours at all, because reflection treats every colour the same. The two bends do the splitting.4
The differences are tiny, as this table of water's refractive index (how strongly it bends light) shows.4 They're still big enough to spread the bow over about two degrees of sky:
*Angle from the point opposite the Sun, worked out from the refractive index with the law of refraction. Sources round these to 42° for red, 40° for violet, and about 50° for the secondary bow.1510
Why red is on the outside
Here's the part most diagrams skip: each raindrop sends only one colour to your eye. Every drop sprays out all the colours, but only one of them heads in exactly the right direction to reach you. Higher drops (at 42°) send you red. Lower drops (at 40°) send you violet. The colours in between come from the drops in between.511 That's why a rainbow is built from millions of drops, and why red sits along the top.1
How many colours are there? A rainbow is a smooth blend, but people usually name seven: red, orange, yellow, green, blue, indigo, violet ("Roy G. Biv"). Many scientists think indigo is too close to blue to count, so six is also common.94
Why are rainbows curved?
A rainbow is centred on the antisolar point: the spot directly opposite the Sun, where the shadow of your head points.96 Every drop that sits 42° away from that spot sends you red light. All the points 42° from one centre form a circle, so the rainbow is really a ring of light around the shadow of your head.10
From the ground, the horizon cuts off the lower part of the ring, so you see an arc.1 How much of it you see depends on the Sun's height:311
That's why you rarely see a rainbow around midday in summer.6 The angle never changes, so a rainbow always has the same size in the sky, however near or far away the raindrops are.11
Is a rainbow a full circle?
Yes. From an airplane, with drops below you as well as above, you can sometimes see the whole ring.167 You can't see rainbows from space, though, because there are no raindrops up there. Nearly all the water in the air stays in the lowest layer of the atmosphere.7
Everyone sees their own rainbow
A rainbow isn't an object sitting in one place. It's light reaching your eye from a certain angle.1 Move, and your antisolar point moves with you, so the rainbow moves too. A friend standing next to you has their own antisolar point and their own horizon, so they see light from a different set of drops: a slightly different rainbow.9 That's also why you can never reach the end of a rainbow. The pot-of-gold story goes back at least to a 17th-century Irish saying.3
Double rainbows
Sometimes a second, fainter bow appears above the first. It's made by light that bounces twice inside each drop before it gets out.110
- Bigger: it comes out at about 50° from the antisolar point, so it forms a larger circle outside the main bow.110
- Colours reversed: red on the inside (bottom), violet on the outside (top).15
- Fainter: some light escapes at every bounce. The secondary bow is roughly a tenth as bright as the primary.67
Look between the two bows and the sky is noticeably darker. Light bounced once inside the drops brightens the sky inside the primary bow, and light bounced twice brightens the sky outside the secondary bow. Neither sends light from the gap between them. This darker strip is called Alexander's dark band, after Alexander of Aphrodisias, who described it around the year 200.12
More bounces make even fainter bows. Third and fourth bows appear towards the Sun and are very hard to see in nature. In the lab, scientists have detected a 200th-order rainbow.96
Other kinds of rainbow
- Moonbows: moonlight (which is reflected sunlight) can make a faint rainbow at night, best when the Moon is bright and low.911
- Fogbows: fog droplets are much smaller than raindrops, so fogbows look pale, almost white.119
- Sea-spray bows: salt water bends light a little more, so these rainbows are slightly smaller.9
- Supernumerary bows: faint pastel bands just inside the main bow, caused by light waves interfering with each other.10
Try it at home: make your own rainbow
On a sunny morning or late afternoon, stand with your back to the Sun and spray a fine mist from a garden hose or sprinkler in front of you. Look about 42° away from the shadow of your head and a rainbow appears in the spray. Waterfalls and lawn sprinklers make rainbows for exactly the same reason as rain.84
Related explainers: the same sunlight that the raindrops split is scattered by air to make the blue sky: see
Why is the sky blue? And to see how colours of light add up to white (and how paints mix differently), try
How does color mixing work?
Common misconceptions
"A rainbow is a thing in a place, and you could walk to its end." It's light arriving at a certain angle, so it moves with you. You can never reach the end.
19
"Everyone sees the same rainbow." Each person has their own antisolar point and horizon, so each sees light from different drops.
9
"Each raindrop contains a tiny rainbow that you see." Each drop sends just one colour to your eye. The full bow is built from millions of drops.
5
"Rainbows are arcs." They're circles. The ground hides the lower part.
13
"The bounce inside the drop splits the colours." Reflection treats every colour the same. The bending on the way in and out does the splitting.
4
FAQ
How is a rainbow formed, in short?
Sunlight enters a raindrop and bends (refraction), bounces off the back of the drop (reflection), and bends again as it leaves. Each colour bends by a slightly different amount, so white sunlight spreads into its colours. Drops about 42 degrees from the point opposite the Sun send red light to your eye, and drops at about 40 degrees send violet. Together, millions of drops make the coloured arc.
Why is a rainbow curved?
You see rainbow light only from drops at a fixed angle, about 42 degrees, from the point directly opposite the Sun (the shadow of your head). All the points at the same angle from a centre make a circle. The ground hides the lower part, so from the ground you usually see an arc.
Why are rainbows so rare?
You need several things at once: bright sunlight behind you, rain or spray in front of you, and a Sun no higher than about 42 degrees. That's why rainbows are most common in the morning or late afternoon after a shower, and rare at midday.
How rare is a double rainbow, and what causes it?
The second bow is often there, but it is only about a tenth as bright as the first, so it is easy to miss. It comes from light that bounces twice inside each raindrop. It appears at about 50 degrees, outside the main bow, with its colours in reverse order.
Can you ever reach the end of a rainbow?
No. A rainbow isn't an object in one place. It is light arriving at your eye from a particular angle, so when you move, the rainbow moves with you. Everyone sees their own rainbow from their own set of raindrops.
Is a rainbow a full circle?
Yes. A rainbow is really a circle centred on the point opposite the Sun. From the ground the horizon cuts it off, but from an airplane you can sometimes see the whole ring.
How many colours are in a rainbow?
A rainbow is a smooth spread of colours with no sharp edges. People usually list seven: red, orange, yellow, green, blue, indigo and violet ("Roy G. Biv"). Many scientists think indigo is hard to tell apart from blue, so you'll often see six listed.
Sources
- NOAA SciJinks, What Causes a Rainbow? (also published by NOAA NESDIS)
- NOAA NESDIS / NASA Space Place, What Causes a Rainbow?
- National Weather Service (Flagstaff), How Do Rainbows Form?
- OpenStax, College Physics 2e, 25.5 Dispersion: The Rainbow and Prisms
- University of Illinois WW2010, Rainbows and Secondary Rainbows
- HyperPhysics (Georgia State University), Primary and Secondary Rainbows
- University of Nevada, Reno, Ask the Professor: How do rainbows form?
- The Physics Classroom, Rainbow Formation
- National Geographic Education, Rainbow
- Encyclopaedia Britannica, Rainbow
- Australian Bureau of Meteorology, How do rainbows form?
- Atmospheric Optics (Les Cowley), Alexander's Dark Band