Further thoughts on Newton’s zero-order rainbow

Abstract

A zero-order rainbow angle may be defined as the relative minimum angle of deviation of geometrical light rays transmitted without internal reflections through a transparent particle. If the incident rays are parallel and the particle is a sphere, such a minimum does not exist. But if the incident rays are not parallel or if the particle has an elliptical rather than circular cross section, an angle of minimum deviation, hence a zero-order rainbow, can occur. For a spherical water droplet, the zero-order rainbow will occur when a point source is placed less than a droplet radius away from its surface. If a column of water with an elliptical cross section is illuminated by a plane wave, a zero-order rainbow will occur if the length of the major axis of the cross section is more than twice the length of the minor axis.