We extend the classical dielectric image problem for an external point char
ge interacting with a semi-infinite medium to the case of an anisotropic di
electric; We show that the exterior potential is a solution to an unconvent
ional image problem. By contrast the interior potential is not a solution t
o any simple image system; instead it can be obtained through an anamorphic
transformation of an image solution. We calculate the volume bound charge
density that is induced within the anisotropic dielectric and distinguishes
it from an isotropic medium where the volume density vanishes. This soluti
on provides a very simple and physically relevant example in which the phys
ics of the surface and volume bound charge densities in a polarized dielect
ric can be analyzed. (C) 2001 American Association of Physics Teachers.