How Do Rainbows Form? How Sunlight and Water Make Colour

Sunlight looks white, but it contains many wavelengths of visible light. When light passes from air into water, its speed changes and the ray bends. This bending is called refraction. Different wavelengths bend by slightly different amounts, which begins to separate the colours.

Inside the droplet, some of the light reflects from the back surface. It then travels back toward the front of the droplet and refracts again as it leaves the water. By the time the light reaches your eye, the colours have spread out enough for you to see them separately. Red appears on the outer edge of a primary rainbow, while violet appears closer to the inner edge.

This sequence is the central answer to how rainbows form. A single droplet does not send a complete miniature rainbow into your eye from every direction. Instead, different droplets send different colours toward you at particular angles. Your brain combines light from huge numbers of droplets into one bright arc.

To see a primary rainbow, the Sun needs to be behind you and water droplets need to be in front of you. The rainbow forms around the point in the sky directly opposite the Sun. That geometry is why rainbows are often seen when a shower is moving away and sunlight breaks through behind the observer.

A rainbow is actually part of a circle centred on that opposite point. From the ground, the horizon usually blocks the lower part, so you see an arc. From a high viewpoint such as an aircraft, it is sometimes possible to see much more of the circle because fewer parts are hidden by the ground.

The exact droplets creating the rainbow for you are not the same droplets creating it for someone standing somewhere else. Move your position and the viewing geometry changes. This is a useful detail when learning how rainbows form because it explains why a rainbow has no fixed location that you can simply walk up to.

A secondary rainbow can form when light reflects twice inside a droplet before leaving. This extra reflection sends the light out at a different angle and reverses the colour order, so red appears on the inner edge and violet on the outer edge of the secondary bow. The extra reflection also loses more light, making the second rainbow fainter.

Large, nearly spherical droplets can produce bright, well-separated colours, while very tiny droplets can make the rainbow look paler. Sometimes extra faint bands appear just inside the main bow because light waves interfere with one another. These are called supernumerary bows.

When you revise how rainbows form, focus first on the three main processes: refraction, internal reflection, and dispersion. Once those are clear, the shape, colour order, and location of a rainbow follow naturally from the path that light takes through millions of droplets.

Light leaving a droplet after one internal reflection is most concentrated at an angle of about 42 degrees from the point directly opposite the Sun. That fixed angle explains when you can see a rainbow. If the Sun is higher than about 42 degrees above the horizon, the whole primary bow would sit below the horizon, so from flat ground rainbows are mostly seen in the morning or later in the afternoon. The secondary bow sits at about 51 degrees, and the sky between the two bows looks noticeably darker, a gap known as Alexander's dark band.

Many people learn that a rainbow has exactly seven colours, but the spectrum is continuous, shading smoothly from red to violet with no real boundaries. The number seven comes largely from Isaac Newton, who divided the spectrum into seven named colours partly by analogy with the seven notes of a musical scale. That is why indigo appears in the familiar list even though many people struggle to pick it out. Other cultures have named different numbers of rainbow colours, a reminder that the bands owe as much to language and habit as to physics.

For centuries the rainbow was one of the hardest puzzles in natural philosophy. A key step came in the early fourteenth century, when two scholars working independently had the same idea. In Persia, Kamal al-Din al-Farisi, and in Germany, the Dominican friar Theodoric of Freiberg, used large glass spheres filled with water as enlarged raindrops. By shining light into them and watching where it emerged, they showed that each bow came from light bending, reflecting inside the drop and bending again, with one reflection for the primary bow and two for the secondary.

What they could not explain was why the bow sits at one particular angle. In 1637 Rene Descartes tackled this with patient geometry, calculating the paths of many parallel rays through a single drop. Most rays leave in scattered directions, but he found that a large number bunch together close to one angle, and that crowding of rays is what makes the bright arc stand out from the sky around it. Explaining the colours fully had to wait for Isaac Newton's prism experiments, which showed that white light is a mixture and that each colour bends by its own amount.

Droplet size changes a rainbow dramatically. In fog or thin mist, where droplets are far smaller than raindrops, light spreading out around each tiny droplet by diffraction smears the colours together. The result is a fogbow, a broad, ghostly white arc, sometimes with faintly coloured edges. You are most likely to see one with the Sun low behind you and a bank of fog ahead, for example from a hillside or a ship. Moonlight can make a rainbow too, called a moonbow. Its colours are real, but the light is usually too dim for the eye's colour-sensing cells, so it looks pale or white.

Rainbow light also hides a surprising property: it is strongly polarised, meaning its light waves vibrate mainly in one direction, running along the arc. This happens because the reflection inside each droplet occurs at an angle close to the one at which reflection strongly favours a single direction of vibration, known as Brewster's angle. You can test this with polarising sunglasses. Look at a bright rainbow and slowly tilt your head, or rotate the lenses, and parts of the arc fade almost completely while others stay bright. Photographers use polarising filters for the same reason, either to strengthen a rainbow against the sky or to remove it.

Sunlight refracts as it enters water droplets, reflects inside them, and refracts again as it leaves. Because different wavelengths bend by different amounts, the light spreads into colours. The geometry places the rainbow opposite the Sun, with countless droplets each contributing light to the arc you see.