I would like to thank E. Blaise Saccocio for the beautiful picture of the double rainbow in the November 2003 issue of Physics Today Physics Today 0031-9228 56 11 2003 10 https://doi.org/10.1063/1.1634511 (page 10) . However, he is incorrect when he states that the dark zone (known as Alexander’s dark belt) between the rainbows is due to interference.
The dark belt can be understood from geometrical optics. The primary (lower) rainbow represents an extreme value of the angle at which light rays are scattered after being internally reflected once by a raindrop. If a viewer on the ground looks at the top of the primary rainbow, and then lifts her head a little higher, she sees a dark sky because no light rays emerge from water droplets at angles steeper than the rainbow angle. The sky is not completely dark in the belt because of scattering due to more than one internal reflection and to light from the sky and the landscape. 1
One rainbow phenomenon that must be explained by interference is the presence of supernumerary bows beneath the primary rainbow. A partial explanation of that phenomenon was given in 1838 by George Airy. 2 If you look carefully, you can see one supernumerary bow (the narrow white band) underneath the primary one in Saccocio’s photo. As with many topics related to rainbows, the supernumerary bow is still actively researched. 3
