Analysis of the refraction of the extraordinary ray in a plane-parallel uniaxial plate with an arbitrary orientation of the optical axis.

Ray tracing formulas in a plane-parallel uniaxial plate bounded by an isotropic medium are analyzed when the crystal axis lies in the incident plane, and when its orientation is arbitrary.We present the behavior of the critical angle for the extraordinary ray as a function of the crystal axis position with respect to the normal to the refracting surface. We give the conditions in order to obtain the incidence angle at which the ordinary and extraordinary ray have the same refraction angle into the uniaxial crystal for particular positions of the optical crystal axis, also we give a condition for normal incidence in order to maximize or minimize the separation between the ordinary and extraordinary ray as a function of the optical crystal axis.