Abstract: The phenomenon of birefringence may be observed when light arrives at an anisotropic crystal surface and refracts through it, causing the incident light ray to split into two rays; these become polarized in mutually orthogonal directions, and two images are formed. The principal goal of this paper is the study of the directional issues involved in the behavior of light when refracting through a homogeneous, non-participating medium, including both isotropic and anisotropic media (uniaxial and, for the first time, biaxial). The paper focuses on formulating and solving the non-linear algebraic system that is obtained when the refraction process is simulated using the geometric model of Huygens. The main contribution focuses on the case of biaxial media. In the case of uniaxial media, we rely on symbolic calculus techniques to formulate and solve the problem.