A simple geometric construction is derived for the shape of the wave front in a homogeneous anisotropic medium. It is shown to be equivalent to the intuitive method of constructing a wave front using Huygen's principle.
Although this construction has been referred to and tersely described in the literature (Musgrave, 1970; Kraut, 1963; Duff, 1960), it is instructive to demonstrate its relationship to the common notion of the wave front obtained via consideration of the group velocity. The wave front is shown to be the polar reciprocal of the slowness surface (the dispersion relation at constant frequency). An appreciation of the pole-polar correspondence between the two surfaces allows quick inference of some of the important features of the wave front in a homogeneous anisotropic medium.