Ray-Tracing Formulas for Uniaxial Crystals

Formulas have been derived relating the direction vector of the extraordinary ray in a uniaxial anisotropic medium to the ordinary ray. With these formulas one can trace rays through uniaxial crystals. Tracing rays into the crystal involves finding the ordinary ray by using the usual ray-tracing formula for isotropic media, then by using the derived equations to find the extraordinary ray. To trace an extraordinary ray out of the crystal, one first constructs the fictive ordinary ray corresponding to it through its point of contact with the refracting surface. Using the ray-tracing formula for isotropic media one traces this ray through the surface.