How are rainbows formed?

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For the grown-up

The short answer. Out of sunlight and raindrops. Sunlight looks white, but it is every color mixed together. When a sunbeam goes into a round raindrop it bends, bounces off the back and bends again on the way out, and each color bends a little differently, so the colors come out spread apart. Each drop sends just one color to your eye, and millions of drops together make the bow, always on the side of the sky across from the sun.

A rainbow is not a thing hanging in the sky. It is sunlight that millions of raindrops have turned around and sent back to you, sorted by color. Here is what one drop really does, where the pictures stop being true, what to ask, and how to make a rainbow in the garden.

How a rainbow is made

Sunlight. It looks white, but it is every color mixed together. Isaac Newton showed this in 1666 by passing sunlight through a glass prism.
In. When light goes from air into water it changes direction: it bends. Each color bends by a slightly different amount, so inside the drop the white beam starts to come apart.
Off the back. Part of the light bounces off the inside of the drop’s far wall. That is why the light comes back toward the side the sun is on.
Out. It bends once more as it leaves. By now it has turned most of the way around, and the colors leave in slightly different directions: red about 42 degrees off the line the sunlight came in on, violet about 40.
One color from each drop. Because the colors leave in different directions, only one of them reaches your eye from any one drop. Drops higher in the sky send you red and yellow. Lower drops send you green and blue.
A bow. Every drop that is 42 degrees away from the point straight opposite the sun sends you red, and those drops make a circle around that point. The ground hides the bottom of the circle, and what is left is a bow.

The numbers

42 degrees for red and 40 for violet, measured from the point exactly opposite the sun. The whole band of colors is only about 2 degrees wide.

The point opposite the sun is easy to find: it is where the shadow of your own head falls. The bow is the same distance from it all the way round.

When the sun is more than 42 degrees up, the whole bow is below the horizon. That is why rainbows belong to mornings and late afternoons, and are rare at midday.

Where the pictures stop being true

The wide colors: On pages 3, 4 and 5 the colors spread over 18 degrees so that small eyes can tell them apart. In the sky they fit into about 2.
Six colors: The colors run into each other with no lines between them, and how many you count depends on the rainbow and on you. Newton listed seven. It is unusual to make out all seven, and his “indigo” is what most people now call blue. The purple here is the one books call violet.
The sun and the bow in one picture: Page 2 shows the sun, the child and the rainbow together. Nobody ever sees that: the bow is always on the side of the sky opposite the sun. Read that page as a map of where things are. The sun is behind the child and the rain is in front.
“A sunbeam”: Real sunlight does not arrive as one thin beam. It floods the whole drop, and light comes back out over every angle from 0 to 42 degrees. It is brightest right at 42, and that bright edge is the bow. The fainter light inside it is why the sky is brighter inside a rainbow than outside. Both paintings of the bow show this.
“Bounce”: Only part of the light bounces. The rest goes straight on out of the back of the drop. Some bounces twice before it leaves, and that light makes the second, fainter bow you sometimes see above the first, about 50 degrees out, with its colors the other way up.
“Tiny balls of water”: True of small raindrops, under about a millimetre in radius. Bigger ones are shaped more like a hamburger bun. None are shaped like a teardrop.
“The colors stay”: Each drop adds to the color for only about a second as it falls, and another takes its place. The rainbow you are looking at is made of different drops from the one you saw a moment ago.
“Your shadow points to the middle”: True for everybody, which means that everybody has their own rainbow. The person next to you sees one made by other drops. It is also why you cannot walk to the end of it: the rainbow is not in one place, and it moves when you do.
“A whole circle”: Every rainbow is a circle. From the ground the land is in the way. From an aircraft or a tall building the circle can close, and it can with a garden hose too, because the drops are between you and the grass.

Questions to ask

Before you start: “Where do you think the colors come from?” Let the guess stand, then find out together.
“Where was the sun when we saw the rainbow?” Behind us. It always is.
“Which color is on top?” Red, every time.
“Could we walk to the end of the rainbow?” No. It moves when we move.
“What happens to the rainbow when the rain stops?”

Try it

Make one with the hose. On a sunny day, stand with the sun at your back and spray a fine mist into the air in front of you. Early morning or late afternoon is easiest. A sprinkler works too.
Find your shadow first. When the sun is out and it is raining, turn until your shadow lies straight ahead of you. If there is a rainbow, that is where it is.
Red on top. Check the next rainbow you see, in the sky or in a picture book.
Look for the second bow. It is above the first one and fainter, with red on the bottom.
Brighter inside. Compare the sky inside the bow with the sky outside it.

Look at your shadow, not at the sun

Nobody needs to look at the sun to find out where it is. Your shadow always points away from it.

Where this comes from

US National Weather Service, Rainbows (light is bent, reflected and bent again; 42 degrees; sun behind you and rain in front; no bow when the sun is higher than 42 degrees; the second bow near 50 degrees, colors reversed).
World Meteorological Organization, International Cloud Atlas, Primary rainbow (violet inside at 40 degrees, red outside at 42; all seven colors are rarely seen; opposite the sun; a complete ring from an aircraft).
HyperPhysics, Georgia State University, The primary rainbow (40 to 42 degrees from the point opposite the sun; rare at midday, most often seen in late afternoon).
Arizona State University, Rainbows, part III (one color from each raindrop; higher drops send red and yellow, lower drops blue and green).
National Geographic Education, Rainbow (not in one spot in the sky; no two people see the same one; full circles; brighter inside; light reflected twice makes the second bow).
Texas Parks and Wildlife, Rainbows (each drop adds its color for only a second and is replaced; the hose, with the sun at your back).
UCAR Center for Science Education, Rainbows (sunlight is a mix of all colors; a hose or a sprinkler; the second bow).
US Geological Survey, Are raindrops shaped like teardrops?
Astro-Canada, The white light spectrum (Newton and the prism, 1666).
Wikipedia, Rainbow (the shadow of your head marks the middle; light returns over 0 to 42 degrees, brightest at 42; about 2 degrees wide; the full circle with a garden hose; Newton’s indigo).

With the sound off, the words stay on the page for you to read aloud.

Every word, page by page

Look! A rainbow! Red. Orange. Yellow. Green. Blue. Purple. How are rainbows formed? Let's find out!
The sun is shining. But there is no rainbow. A rainbow needs rain, too. Tap the cloud. A rainbow! Sunshine and rain, at the same time. Now tap the sun to hide it. No sun, no rainbow! Tap the sun again to bring it back. There! A rainbow takes both. Sun and rain, together.
Rain is made of tiny balls of water. Here is one raindrop, very big. And here comes a sunbeam. Pull the sunbeam down, into the drop. Bend. Bounce. Bend. Look! Colors come out! The colors were hiding in the white sunlight. The drop bends each color a little differently. So they spread apart.
The colors go different ways. Only one of them reaches your eye. Slide the drop up and down. Up high, the drop looks red. Then orange. Yellow. Green. Blue. And down low, purple.
One drop, one color. But rain has lots and lots of drops! Tap the cloud, again and again. Stripes! High drops send you red. Low drops send you purple. Every color has its place. The drops fall down. New drops take their place. So the colors stay. And that is a rainbow!
Sun and rain, together. So where is the rainbow? Not here! Turn around. Tap. There it is! The sun is behind you. The rain is in front of you. And your shadow points to the middle. Next time you have sun and rain, turn your back to the sun. And look!
Now you make a rainbow, with the hose. The sun is behind you. Spray water with your finger, all around your shadow! You did it! You made a rainbow. And look, it is a whole circle! Spray some more!