Rainbows by elliptically deformed drops. I. Möbius shift for high-order rainbows

Using ray theory, the Möbius shift of the (p-1)-order rainbow angle for a particle having an elliptical cross section is obtained to first order in the ellipticity as a function of the tilt of the ellipse with respect to the propagation direction of the incoming rays. The result is then adapted to the geometry of scattering of light rays from the sun by a falling water drop as a function of sun height angle. The variation in the angular spacing between the supernumeraries is determined as a function of location along the rainbow arc, the conditions under which the rainbow angle is insensitive to drop flattening were determined, and the dependence of the Möbius shift on the drop refractive index is shown for rainbows up to fourth order (p=5).