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Rainbows are sometimes abnormally shaped. The reflection of a rainbow (a reflected bow) may be seen in a smooth water surface, and the reflection of the sun is able to generate a rainbow in the sky. The latter is called the reflection-bow or the reflected-light rainbow.
When a rainbow is reflected, the polarization of its light hardly changes: the plane of polarization is not reflected in the case of such a grazing reflection. Therefore, contrary to the situation with the non-reflected bow, the direction of polarization of the reflected one no longer follows the curvature of the bow. Hence Tangential polarization is now absent. But the rainbow and its reflection can be extinguished almost simultaneously with a polarizing filter in the appropriate orientation. Of course reflection of the rainbow can also be observed by putting a polished metal plate or an ordinary mirror on the ground. Then, the direction of polarization does follow more or less the curvature of the bow, because these materials reflect not only the bow but also mirror the plane of polarization. In these artificial circumstances is the metal plate in particular that additionally converts a part of the line rainbow-light into circularly polarized light: the right part of the reflected rainbow is then left-handed circularly Polarized and vice versa. When a horizontal glass plate or a pane is used as a reflecting surface, the polarization is analogous to the one seen in reflection on water.
Reflection-bows are very rare and usually only sections of them are seen. The polarization of this type of bow is tangentially directed with respect to the reflection of the sun. Hence the polarization follows the curvature of the bow. Some deviations may occur, because the light of the reflected sun is itself horizontally polarized, but generally they will be hardly perceptible. The reflected dew-bow and the reflection dew-bow, which can be seen in ditches, behave in the same way as the reflected rainbow and the reflection-bow so that by finding out whether the polarization follows the curvature of the bow, one can decide which of the two types of bow is seen here.
Under extremely rare circumstances extra bows sometimes appear in the sky in different places. It usually happens near water surfaces. Some of them are reflection-bows but come from reflection on rough water; other ones, however, can not yet be explained satisfactorily. If you should be lucky enough to see such a reflection-bow or another abnormal rainbow take a picture and examine its polarization. Does the polarization direction follow the shape of the bow or not? Is the degree of polarization higher or lower than that of the rainbow itself? Observation of the polarization of this kind of phenomenon may hold the key to the explanation of such remarkable and rare bows.
source: Polarized light in Nature