Polarized rainbow.

The Airy theory of the rainbow is extended to polarized light. For both polarization directions a simple analytic expression is obtained for the intensity distribution as a function of the scattering angle in terms of the Airy function and its derivative. This approach is valid at least down to droplet diameters of 0.3 mm in visible light. The degree of polarization of the rainbow is less than expected from geometrical optics; it increases with droplet size. For a droplet diameter >1 mm the locations of the supernumerary rainbows are equal for both polarization directions, but for a diameter <1 mm the supernumerary rainbows of the weaker polarization component are located between those in the strong component.