The main theories that have been proposed to explain the observed features of the rainbow, from Descartes to the present, are reviewed here. They evolved in close parallel with theories about the nature of light. Surprisingly, as late as 1957, it was pointed out that no reliable quantitative theory of the meteorological rainbow existed at that time (apart from complicated numerical computer calculations).

Geometrical-optic theory

In the rainbow (for color pictures, see Greenler 1980), the primary bow is surrounded by the much fainter secondary bow, in which the colors appear in reverse order. The bows are just sets of directions in the sky, centered around the antisolar point, the direction opposite to that of the Sun: the higher the Sun's elevation, the lower the antisolar point below the horizon, and the smaller the portion of the rainbow arcs seen.

Each of the bows has a bright side and a shadow side, and the shadow sides face each other, so that the sky between the bows looks darker, as was described by Alexander of Aphrodisias around 200 AD (Alexander's dark band).

By means of an experiment performed at the remarkably early date of 1304, it was demonstrated by Theodoric of Freiberg that the rainbow arises from the scattering of sunlight by individual water droplets in the atmosphere.