## Is a quadruple rainbow possible

Question

Yes, although very rare, it is possible for a human to see four natural rainbows at once in the sky. A rainbow occurs when white sunlight scatters off of raindrops in the air. Because of the dispersive properties of water, the different colors of light in the sunlight bend (refract) different amounts when entering and leaving the raindrop. As a result, the different colors leave the raindrop at different angles, making you see the different colors at different locations in the sky. Because this scattering is a geometric effect that depends on the direction of the original incoming sunlight, the rainbow forms as a circle (or part of a circle) that is centered on the point exactly opposite of the sun. The main rainbow (called the “primary rainbow”) involves sunlight entering the raindrop, reflecting once off the inner back surface of the raindrop, and then exiting the raindrop.

Additionally, light can bounce twice off the inner surface of the raindrop before exiting. The second reflection causes these light rays to exit at an angle that is very different from that of the light rays that only reflect once. Therefore, a secondary rainbow forms that has a larger radius than the primary rainbow. The secondary rainbow is created by the same sunlight and the same refraction process as the primary rainbow, so it is also centered on the point exactly opposite the sun. Because of the additional reflection, the colors in the secondary rainbow are reversed in order compared to the primary rainbow. Since some light is lost out of the raindrop with every reflection, the secondary rainbow is much fainter than the primary rainbow. In principle, the secondary rainbow is always present. However, the secondary rainbow is often so faint that humans can’t see it. When viewing conditions are right (i.e. it is an unusually sunny day and there are an unusually high number of raindrops in the air), the secondary rainbow can be seen quite distinctly.

The primary and secondary rainbows are visible in this photograph. Public Domain Image, source: NASA.

As you may have guessed, light can bounce three times off the inner surface of the raindrop before exiting, creating a third-order rainbow; or bounce four times, creating a fourth-order rainbow; and so on. However, the third-order and higher-order rainbows are so faint that they are almost never seen by the naked eye. By using a camera and image enhancements techniques, the third-order rainbow can indeed be imaged. This task is difficult enough that successfully capturing and analyzing the third-order rainbow earned Michael Grossman, Elmar Schmidt, and Alexander Haussmann a publication in the academic journal, Applied Optics. Considering the near impossibility of seeing third- and fourth-order rainbows, how are people able to see four rainbows in the sky at once?

The answer is that some of the sunlight can be reflected before entering the raindrops. Recall that rainbow formation is a geometric scattering effect leading the rainbow to be centered on the point opposite the sun. What would happen if there were two suns at two different locations in the sky? Then sunlight would hit the raindrops at two different angles, and two primary rainbows would result, each centered on a different point. If viewing conditions are favorable enough that the secondary rainbows are visible, then there would be four rainbows: a primary rainbow and a secondary rainbow centered on the point opposite the one sun, as well as a primary rainbow and a secondary rainbow centered on the point opposite the other sun. On planets with rain and two suns, quadruple rainbows are common. However, we don’t have two suns, so why am I mentioning this? A large, flat, shiny surface can reflect enough sunlight that the situation acts like two suns. A calm lake does exactly this. The sunlight coming directly from the sun is at an angle that is different from that of the sunlight reflecting off the surface of a lake, and they therefore form different rainbow sets centered on different points. The rainbows formed from the sunlight coming off of the lake are called “reflection rainbows”. In summary, although it is very rare, it is possible for the naked human eye to see four natural rainbows at once in the sky, consisting of:

The primary rainbow (single reflection inside the raindrop) from direct sunlight.
The secondary rainbow (double reflection inside the raindrop) from direct sunlight.
The primary rainbow (single reflection inside the raindrop) from lake-reflected sunlight.
The secondary rainbow (double reflection inside the raindrop) from lake-reflected sunlight.

In principle, the naked human eye could see six rainbows if there were two different large reflecting surfaces, creating the effect of three suns. For instance, if a large, flat, smooth glacier was sitting next to a lake and its surface was tilted compared to the lake’s surface, then if conditions were just right, you could see six rainbows at once. Although physically possible, this situation is exceedingly rare.