New ideas and calculations about angles are presented, particularly about the degree of polarization of the first twenty rainbows, and it is proved why never more than two rainbows can be seen in the sky. The general sky brightness of the rainbow neighborhood is calculated with the Fresnel reflection formulas. It is shown that for certain refraction indices the first one or each of the higher rainbows can be polarized completely and that with a rising n there is an upper limit of existence for each one of them. This is clearly shown by diagrams. The standard of the exact color finding on rainbows is described with special emphasis on the fact that the loss of saturation, due to light reflected by waterdrops, must be considered. Some special features of rainbows mentioned in literature are pointed out and the importance of this phenomenon in constructive art, folklore, and religion is discussed.
S. Rösch, "Der Regenbogen in Wissenschaft und Kunst," Appl. Opt. 7, 233-233 (1968)