A page from the "Causes of Color" exhibit...
Why are rainbows colored?
How is a rainbow formed?
The mechanics of rainbows have been studied since ancient times. The Greek philosophers were aware of the role of reflection in forming a rainbow, and had some understanding of the role of refraction. In the 13th century, scientists produced theories on rainbow formation, and in the 17th century, Rene Descartes sketched out the conditions required to observe a rainbow.
We see rainbows because of the geometry of raindrops. When the sun shines from behind us into the rain, incident rays of light enter the drop and are refracted inwards. They are reflected from the back surface of the raindrop, and refracted again as they exit the raindrop and return to our eyes. Refraction is responsible for splitting the sunlight into its component colors.
Above, compare the angles from internal and double-internal reflections. There are triple- and quadruple- internal reflections as well. See up to 6 internal reflections below.
Secondary rainbows are formed by double internal reflection. Light is reflected twice from the inner surface of the raindrop before leaving the raindrop. The light is concentrated between approximately 50.4° and 53.6°, forming a secondary rainbow above the primary rainbow.
The size of the raindrops does not affect the geometry of the rainbow, although very tiny drops, such as those in fog or mist, reduce the effect. In this case, the effect of scattering overpowers the dispersive refraction effect. A "fogbow" has the arc of a rainbow, but appears as a bright white bow without spectral colors.
The angle of the sun does affect the rainbow we see. Once the sun is higher than 42°, the rainbow arc slips below the horizon. As the sun approaches the horizon, the size of the visible arc increases, reaching a full semicircle just before sunset.
Moonbows have been observed, but as our night vision is not sensitive to color, they appear white rather than colored.
Secondary rainbows and supernumerary rainbows
If one rainbow is beautiful, a double rainbow is breathtaking. In fact, is possible for sunlight to be reflected three or more times in one raindrop, but third order rainbows cannot be seen. They form so close to the sun that its brightness overpowers them.
In the laboratory, it is possible to recreate multiple rainbows formed by multiple internal reflections. A spherical flask of water simulates the raindrop.
In a double rainbow, raindrops reflect the sun’s light noticeably inward from the rainbow arc, and correspondingly out of the secondary bow, so that the dark band is seen between the bows. This effect, called Alexander’s band, was first described by the Greek philosopher Alexander of Aphrodisias in the 3rd century. The sky below the primary (lower) rainbow, and above the secondary (higher) bow, is brighter as a result.
A supernumerary rainbow forms additional bands on the inner arc of the primary rainbow, or very occasionally on the outer arc of the secondary rainbow. These bands, which usually appear in pastel colors, are caused by the interference of light waves.