A rainbow looks like an object, an arch of color stretched across the sky, and it needs sunshine and water drops in the air, such as rain. To see a rainbow, the sun must be behind you and the water drops in front of you, and a rainbow is not a thing in one place in the sky, and it is light that reaches your eyes only when you stand in the right spot. 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. Two people standing side by side therefore observe slightly different rainbows, each made by its own set of drops.
The spot exactly opposite the sun, called the antisolar point, is the center of the rainbow's circle, and the main bow forms where you look about 42 degrees away from it. A rainbow is round because every direction that is 42 degrees from the antisolar point makes a circle around it, and a rainbow is really a full circle, although the ground usually hides the lower part, so we see only an arc. The light that you receive comes from the direction of the raindrops, not from the sun. In this description, the center of the circle is a point in the sky, the radius is 42 degrees, and the observer stands at the apex of the cone that links the two. Taken together, these statements fix the bow completely: its center is opposite the sun, its angular radius is 42 degrees, and the visible part depends on how much of the circle the horizon hides.
The higher the sun is in the sky, the lower the rainbow sits and the less of its arch you can see. If the sun is more than 42 degrees above the horizon, no rainbow can be seen from the ground. A red rainbow shows when the sun is very low, near sunrise or sunset, because scattering in the long path through the air removes the blue and green light and leaves mostly red. Air molecules scatter short wavelengths such as blue and violet more strongly than long wavelengths such as red, which is also why sunsets look red, and the sun's height therefore affects both how much of the circle can be seen and what color the light is. The same sun that sets the height of the bow also sets how red the light has become, since a low sun means a long path through the air for its light.
Sunlight looks white, but it is made of all the colors of the rainbow mixed together, and a prism is a piece of glass that splits a beam of sunlight into rainbow colors. Light bends when it goes from air into water, and this bending is called refraction, and light moves more slowly in water than in air, which is why it bends when it enters a raindrop. Sunlight enters a raindrop, bends, bounces off the back of the drop, and bends again as it leaves, heading back toward the sun's side of the sky, and that path has three steps, an entry, a reflection and an exit, and the bending happens at the first and the last. Each of those steps changes the direction of the light, and the final direction is what decides where an observer must look to receive it.
More exactly, raindrops are not prisms: they are nearly round, and the light separates because it is bent twice at curved surfaces of the drop. Different colors of light bend by different amounts when they enter water, so the colors spread apart, with violet bending the most and red the least. Red has the longest wavelength of visible light and violet the shortest, and human eyes can see wavelengths of light from about 380 to 700 nanometers, and the index of refraction of water changes with wavelength, which is why the drop spreads sunlight into colors. Dispersion means light is spread out by wavelength, and reflecting off the back of a drop does not disperse light, because reflection does not depend on wavelength. Each of these statements concerns one drop, but the rainbow itself is made by a huge number of drops, each of which supplies light of one color to a given observer.
Red light leaves a raindrop turned about 42 degrees from the sunlight's path and blue-violet light about 40 degrees, so the colors line up in bands. Every raindrop sends out all the colors, but each drop sends different colors in different directions, so your eye catches just one color from each drop. Red light comes out of the drops at a steeper angle than blue light, so you see red from drops higher up, at the top and outer edge of the bow, and blue from lower drops. In the main rainbow the colors always come in the same order, with red on the outside and blue and violet on the inside. A rainbow is really a smooth, continuous range of colors, and Isaac Newton popularised the idea of seven, and many scientists think indigo is too close to blue to tell apart, so some modern lists merge indigo into blue and violet. A continuous range means that colors run into each other with no sharp edges.
Light leaves a raindrop in many directions, but the most light is concentrated near 42 degrees, and 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. In Descartes' ray theory, a rainbow forms where the angle of the rays leaving the drop reaches an extreme value, a turning point. The turning point is the angle at which the rays stop spreading further and begin to turn back, which is where they pile up. The rainbow ray is the one that comes out turned the least of all, and the crowding of rays near that smallest turn is the property that the later wave theories had to refine.
The ancient Greek thinker Aristotle explained the rainbow as sunlight reflecting off a cloud, which is not right. Around 1300, scholars in Persia and Germany worked out that a rainbow comes from light refracted and reflected inside single raindrops. Theodoric of Freiberg, in Germany, studied rainbows with a globe of water, treating it as a magnified raindrop. In Persia, Kamal al-Din al-Farisi studied the rainbow by filling a large glass vessel with water and putting it in a camera obscura, to stand in for one giant raindrop. In 1637 René Descartes explained the rainbow by tracing light through a raindrop, and with Newton he set up the basic ray theory of the rainbow. These steps run in a clear order, from a magnified drop in a vessel of water, to a traced ray, to a ray theory, each step making the picture of one drop more exact.
Theodoric also explained the double rainbow: the extra reflection reverses the order of the colors and weakens the light. In a double rainbow, the second bow is outside the first, and its colors are in reverse order. It comes from light that reflects twice inside the drop and leaves at about 50 to 51 degrees, wider than the primary bow, and sometimes two rainbows show at once, a bright one and a fainter one above it with its colors flipped. A third-order, or tertiary, rainbow is a different case, and it is centered on the sun itself, so you have to face the sun to look for it, and it is very faint. The reversal of colors and the wider angle together identify the second bow as the result of two reflections, in the same way that the first bow results from one.
The dark strip of sky between the two bows is called Alexander's band, after Alexander of Aphrodisias, a Greek philosopher who studied it around 200 AD in connection with Aristotle's incorrect theory. The band between the two bows is dark because almost no sunlight is scattered toward your eyes from that part of the sky. The band lies between the primary bow, at about 42 degrees, and the secondary bow, at about 50 to 51 degrees, so it occupies a gap of roughly eight or nine degrees of sky between the two arches. Alexander studied the band around 200 AD, whereas the globe and vessel experiments came around 1300, and the word band here means the strip of sky itself, which is darker than the bows on either side of it
Before Newton, many people thought a prism changed sunlight and made the colors. In the mid-1660s Isaac Newton used glass prisms to show that white light is made of a spectrum of colors. Newton let a beam of sunlight pass through a prism onto a wall, and then 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 the prism separates them because each color bends by a different angle. Newton's tests therefore changed the question from whether glass makes color to how white light is built from colors that a prism sorts by angle. The second prism brought the white light back.
In his crucial experiment, a board with a hole let only one color, such as red, pass into a second prism, and that light bent but stayed the same color, so a prism does not make colors, it only bends each color by a different amount. Newton also used a lens to bring a spread-out spectrum back into one beam, and the merged beam was white. Passed through another prism, it split into a spectrum again. He explained the rainbow as sunlight refracted and reflected by raindrops that act as tiny prisms, adding the spreading of colors to Descartes's raindrop picture, and lenses bend each color by a different amount, so a lens telescope shows colored fringes around a star. This blur is called chromatic aberration. In effect, the lens did for the whole spectrum what the second prism had done for the beam of sunlight.
The simple ray picture of Descartes and Newton explains the main bow but not the faint extra bands, and those need the wave nature of light, and sometimes faint extra pastel arcs, called supernumerary bows, show just inside the main rainbow. Supernumerary bows come from interference: light waves that add together where they match and cancel where they do not. They show up best when raindrops are small and nearly the same size. Bigger drops make narrower, more closely spaced supernumerary bands, and smaller drops make wider, more widely spaced ones. With large drops the extra bands fall inside the colors of the main bow and are hidden, and the faint bands depend on the size of the drops, so their appearance reports something about the water in the air. Each of those faint bands is therefore a small sign that the light has wave properties.
In 1803 Thomas Young explained supernumerary bows as interference between light waves, which helped the wave theory of light win acceptance. Young's interference idea was only an approximation. George Airy worked out the full wave theory of the rainbow more than 30 years later. Rainbow light is strongly polarized. David Brewster showed in 1812 that it is almost completely polarized, and a modern measurement found up to 94 percent. Airy's wave theory leaves out polarization. A complete treatment uses Maxwell's equations, and Gustav Mie worked out the exact solution for light scattered by a sphere in 1908, and the exact Mie solution is an infinite series of terms that converges slowly, so physicists use approximations such as Airy theory to understand the rainbow. The progression from Young to Airy to Mie is a progression from approximation to a complete solution, in which each treatment adds something the earlier one omitted.
Fogbows are pale, nearly white rainbows that form in fog, mist or cloud, and they are broad and pale because fog droplets are far smaller than raindrops, so the light spreads out (diffracts) and smears the colors. A glory is a ring of colored light around the shadow of the viewer's head, often seen with fogbows, and it is physically more complex than a rainbow, and it comes from light scattered almost straight back. Rainbows can also be made by moonlight, and these moonbows, or lunar rainbows, are rare. In laboratories, scientists have made rainbows of very high order: a 13th-order one with a laser and a 200th-order one in another experiment (as of November 2026). Scientists describe the rainbow at several levels, from simple ray paths (geometrical optics), to Airy's wave approximation, to the exact Mie theory of light scattering. The levels complement each other, and rainbows have served as a testing ground for theories of light: Descartes's rays, Newton's colors, and Young's waves. Physicists also find rainbows in the way atoms, molecules and atomic nuclei scatter, a pattern with the same mathematics as the rainbow in a raindrop.
Words to know
- antisolar: opposite the sun
- dispersion: spreading by wavelength
- interference: waves adding together
- polarized: light waves aligned
