Symmetries and asymmetries of the refracted and reflected rays in a uniaxial plane parallel plate

In this paper, we present a review and enlargement of the symmetries and asymmetries of the refracted and reflected rays in a uniaxial plane-parallel plate. When the both involved axes of revolution are not coincident, the plane defined by these two axes is a plane of symmetry. But, with respect to a plane which is perpendicular to the incidence plane, the refractive indices are asymmetrical. This gives rise to the asymmetry of the rays’ directions. However, the optical paths result symmetrical. We also analyze the symmetries of the incidence point corresponding to the refracted and reflected rays.