Electric polarization and the extinction of the extraordinary reflected ray

When light is incident from an isotropic medium on to an interface with a uniaxial crystal, the idea of an effective electric polarization is useful. We show that the same idea may be extended to the reverse situation where the light is incident from the uniaxial crystal. In this case, when the optical axis lies in the plane of incidence, there is a Brewster angle associated with the extinction of the reflected ray, because the waves have a definite polarization. We analyse the relation between the Brewster angle and the effective electric polarization at the interface.