For a long time, the rainbow was explained badly, and the ancient Greek thinker Aristotle explained the rainbow as sunlight reflecting off a cloud, which is not right. Before Newton, many people thought a prism changed sunlight and made the colors, and today we say that sunlight looks white but is made of all the colors of the rainbow mixed together. A prism is a piece of glass that splits a beam of sunlight into rainbow colors. A rainbow is a curved band of colors in the sky, and its colors and the colors that come out of a prism are the same, in the same order. In short, the question was whether glass makes color or only reveals the color that is already there.

In the mid-1660s Isaac Newton used glass prisms to show that white light is made of a spectrum of colors. He let a beam of sunlight pass through a prism onto a wall. Then he showed that a second prism brings the colors back together into white light, and people had seen prisms make colors before Newton. His new idea was that white light is a mix of all the colors, and that the prism separates them because each color bends by a different angle. The second prism therefore showed that the first one had added nothing to the light, because the white light came back when the colors were put together again.

The bending has a name in the language of physics, and light bends when it goes from air into water. This is called refraction. Refraction is the bending of a wave as it passes from one material to another, such as light going from air to water. Light moves more slowly in water than in air, which is why it bends when it enters a raindrop. The index of refraction of water changes with wavelength, which is why a drop spreads sunlight into colors. Different colors bend by different amounts, with violet bending the most and red the least, and red has the longest wavelength of visible light and violet the shortest. Human eyes see wavelengths from about 380 to 700 nanometers.

Now picture a single raindrop, and a raindrop is not a prism: it is nearly round. The light separates because it is bent twice at curved surfaces of the drop. Sunlight enters the drop, bends, bounces off the back, and bends again as it leaves, heading back toward the sun's side of the sky. Red light leaves turned about 42 degrees from the sunlight's path and blue-violet light about 40 degrees, so the colors line up in bands. Each ray of sunlight therefore makes a journey of three steps inside the drop, which are in, back and out. The bending on the way in and on the way out is what separates the colors.

A rainbow is not a thing in one place in the sky, and its light reaches you from the direction of the raindrops, not from the sun. The spot exactly opposite the sun, called the antisolar point, is the center of the rainbow's circle. In a rainbow the colors always come in the same order, with red on the outside and blue and violet on the inside. Your rainbow is yours alone: each person has a different shadow point and horizon, and a different set of raindrops makes the rainbow each person sees. This means that what a rainbow looks like depends on where the observer stands, and a different observer, with a different shadow point, receives light from different drops.

Why does the bright arc sit near 42 degrees? Light leaves a raindrop in many directions, but the most light is concentrated near 42 degrees. One special ray, the rainbow ray, has the smallest angle of deviation of all rays entering the drop, and much of the sunlight is focused along it. Because the rays bunch up near that smallest angle, the light there is concentrated, and the concentration is what makes the bright arc of the rainbow. The main bow forms where you look about 42 degrees away from the point exactly opposite the sun, and big raindrops make bright, vivid rainbows, and small drops make paler ones. The sky inside a rainbow is brighter than the sky outside it.

Sometimes two rainbows show at once: a bright one and a fainter one above it with its colors flipped, and a double rainbow follows from the same drop. It happens when light bounces twice inside the raindrops instead of once, so the second bow is outside the first and its colors are in reverse order. The secondary rainbow leaves the drop at about 50 to 51 degrees, wider than the primary bow. Between the two bows lies the dark strip of sky called Alexander's band. It is dark because almost no sunlight is scattered toward your eyes from that part of the sky. A double rainbow is therefore two rainbows, one made by single bounces inside the drops and one made by double bounces.

Sometimes faint extra pastel arcs, called supernumerary bows, show just inside the main rainbow, and fogbows are different: pale, nearly white rainbows that form in fog, mist or cloud. They are broad and pale because fog droplets are far smaller than raindrops, so the light spreads out and smears the colors, and rainbows can also be made by moonlight. These moonbows, or lunar rainbows, are rare, and they are dimmer than rainbows because moonlight is much fainter than sunlight. They usually look white to our eyes, and fogbows form from the same sunlight as ordinary rainbows, but they form from far smaller droplets. Moonlight is much fainter than sunlight, so a moonbow is much dimmer than a rainbow.

Rainbows often show up after a rain shower, when the sun comes out. You can see a rainbow in the spray from a waterfall, a garden hose or a lawn sprinkler. The best chances to see a rainbow are in the early morning or the late afternoon and evening, when the sun is low. The higher the sun is in the sky, the lower the rainbow sits and the less of its arch you can see. At sunset the arch is a half circle with its top about 42 degrees above the horizon. If the sun is more than 42 degrees above the horizon, no rainbow can be seen from the ground.

How many colors does a rainbow hold? The usual order is red, orange, yellow, green, blue, indigo and violet, remembered as ROYGBIV. People usually name six or seven colors in a rainbow. But a rainbow is really a smooth, continuous range of colors, and Isaac Newton popularised the idea of seven. Many scientists think indigo is too close to blue to tell apart, so some modern lists merge indigo into blue and violet. Newton showed the colors are already in the light. The prism only separates them, and the list of seven goes back to Newton, whereas the light itself shows a continuous range.

Words to know

• spectrum: band of colors
• refraction: light bending
• supernumerary: extra, additional
• indigo: deep blue-violet