English poet John Keats famously worried that scientific explanations would “unweave a rainbow”—that by elucidating rainbows and other phenomena rationally, scientists would drain the world of its mystery. Yet if anything, the close study of rainbows enriches our appreciation of them. The multicolored arc is just the beginning. Look closely, and you will see that outside the main bow is a darkened band of sky and a second, dimmer arc, with its colors in reverse order. Inside the main bow are greenish and purplish arcs known as supernumerary bows. The rainbow can vary in brightness along its width or length, and it can split into multiple bows near the top. Viewed through polarizing sunglasses, the rainbow waxes and wanes as you tilt your head.
The basic scientific explanation for rainbows dates to Persian physicist Kamāl al-Dīn al-Fārisī and, independently, German physicist Theodoric of Freiberg in the 14th century. But scientists continued to work on the theory into the 1970s and beyond [see “The Theory of the Rainbow,” by H. Moysés Nussenzveig; SCIENTIFIC AMERICAN, April 1977]. Many textbook explanations of rainbows are wrong, and a thorough description is still elusive. “The rainbow has the undeserved reputation of having a simple explanation,” says atmospheric physicist Craig Bohren of Pennsylvania State University.
The central principle is that each water droplet in the air acts as a mirror, lens and prism, all in one. Droplets scatter sunlight in every direction but do so unevenly, tending to focus light 138 degrees from the incident direction. Those droplets that form this angle with the sun look brighter; together they produce a ring. Typically you see only the top half of this ring because there are not enough drops near the ground to fill out the bottom half. “The rainbow is just a distorted image of the sun,” write atmospheric scientists Raymond Lee, Jr., and Alistair Fraser in their definitive book The Rainbow Bridge.
The angle of 138 degrees means you see the rainbow when standing with your back to the sun. The lensing angle varies slightly with wavelength, separating the white sunlight into colored bands. Multiple reflections within droplets create the outer bows; wave interference accounts for the supernumerary arcs; flattening of the droplets causes brightness variations along the arc; multiple droplet sizes produce split bows; and light is polarized much like the glare on any watery surface.
Even this physics does not touch on how our eyes and brains perceive the continuous spectrum as discrete colors. The weaving of the rainbow occurs in our heads as much as it does in the sky.