The physics of rainbows.

Rainbows appear when sunlight interacts with raindrops in the atmosphere, creating a spectrum of colors arranged in a circular arc. This mesmerizing effect results from the physics of light, involving reflection, refraction, and dispersion. To understand the physics of rainbows, we must explore the behavior of light as it enters and exits water droplets, the role of total internal reflection, and the formation of secondary rainbows and supernumerary arcs.

Light and Refraction

Light is a form of electromagnetic radiation that travels in waves. When light moves from one medium to another—such as from air to water—its speed changes, causing it to bend.

For a rainbow to form, sunlight must enter a spherical raindrop. As it does, different wavelengths (colors) of light refract at slightly different angles due to their varying speeds in water. This phenomenon, known as dispersion, causes white light to split into its constituent colors—red, orange, yellow, green, blue, indigo, and Violet.

Reflection Inside the Raindrop

Once the light enters the raindrop and disperses into colors, it reaches the back of the droplet, where it is internally reflected. This reflection occurs because the angle of incidence at the back of the droplet is larger than the critical angle, preventing the light from exiting the raindrop and forcing it to bounce Back toward the front.

For a primary rainbow, light undergoes a single internal reflection before it exits the raindrop. However, the angle at which the light emerges is different for each color. Red light (longer wavelength) exits at a larger angle (around 42°) relative to the incoming sunlight, while violet light (shorter wavelength) emerges at a smaller angle (about 40°). This separation of colors produces the characteristic rainbow spectrum.

Formation of the Rainbow Arc

A single raindrop does not produce an entire rainbow—only one color from each raindrop reaches an observer’s eye. However, because there are millions of raindrops in the sky, each at different heights and angles, the collective effect is a continuous, curved spectrum. The circular shape arises because light exiting the droplets at the correct angles is always seen at a specific angle relative to the observer’s line of sight.

Rainbows appear opposite to the sun in the sky, with the observer’s shadow pointing toward the center of the rainbow’s arc. If the horizon were not in the way, a full rainbow would be a complete circle, as seen from an airplane or from high altitudes.

Secondary Rainbows and Double Rainbows

Sometimes, a second, fainter rainbow appears outside the primary rainbow. This is called a secondary rainbow, and it is caused by light undergoing two internal reflections inside the raindrop instead of one.

With each additional internal reflection, some light is lost, which makes the secondary rainbow fainter. Additionally, the colors of a secondary rainbow are reversed—red appears on the inner edge, while violet is on the outer edge. This occurs because the second reflection inverts the color sequence before the light exits the raindrop.

Supernumerary Rainbows

In some cases, faint, closely spaced bands appear just inside the primary rainbow. These supernumerary rainbows are the result of wave interference. Unlike the primary rainbow, which is explained by geometric optics, supernumerary rainbows require wave optics to be understood.

When light waves of slightly different wavelengths interfere constructively and destructively, they create alternating bright and dark bands. Supernumerary rainbows are more common in smaller raindrops, as wave effects are more pronounced in such cases.

Rainbows in Different Conditions

Rainbows can appear in various settings beyond rainstorms:

Moonbows: When moonlight (instead of sunlight) is refracted and reflected inside raindrops, it produces a much fainter lunar rainbow or moonbow. Due to the lower intensity of moonlight, moonbows often appear white to the human eye, though long-exposure photography can reveal their colors.

Fogbows: When light interacts with tiny water droplets in fog or mist, a fogbow forms. These rainbows appear pale or white because the small droplet size causes strong diffraction, reducing color separation.

Fire Rainbows: Sometimes mistaken for rainbows, circumhorizontal arcs or fire rainbows occur when sunlight passes through ice crystals in high-altitude clouds rather than raindrops.

Conclusion

The physics of rainbows combines the principles of reflection, refraction, and dispersion to create one of nature’s most stunning visual effects. Light entering raindrops bends, reflects internally, and exits at different angles, producing a spectrum of colors that form a circular arc. Additional phenomena such as secondary rainbows, supernumerary rainbows, and moonbows showcase the complexity of light’s behavior in different conditions. Whether viewed after a storm or in a misty waterfall, rainbows remain a breathtaking demonstration of the laws of physics in action.