Partial Polarization of Rainbows
More brilliant photographs of rainbows may be obtained by using a polarizer on the camera lens, because one finds that the intensity of the rainbow colors is affected by the rotation of the polarizer. While the polarization of the rainbow is not well characterized in the literature, some polarization is evident in the rainbow, particularly in the near vertical parts of the rainbow near the horizon. Any reflected light will be partially polarized by the fact that the reflection coefficients for light parallel and perpendicular to the plane of incidence of the sunlight on the reflecting surface will be different, enhancing one plane of polarization over the other.
The plane of polarization of the rainbow is tangent to the rainbow arc. Lynch and Livingston report "Measurements with a polarimeter show that the rainbow is polarized up to 94%. This polarization arises at the internal reflection in the water drop which is near the Brewster angle. The bright sky inside the primary bow is also tangentially polarized since most of this additional scattered light has taken a similar path through the droplets."
Atmospheric optics concepts
Lynch and Livingston