Exact Result for the Grazing Angle of Specular Reflection from a Sphere

The present paper shows that it is possible to exhibit the grazing angle of specular reflection as one of four angles derived from the zeros of a certain self-inversive quartic polynomial whose coefficients are complex. Thus the grazing angle may now be found deterministically, whereas heretofore it had to be computed either by approximations or numerical procedures. The preceeding analysis shows further that factoring, in a useful way, a quartic polynomial whose complex coefficients depend on even a small number of parameters, is not always a trivial matter, even though the methods of Cardan and Ferrari have been known for centuries.