In vector form, if "'i "'is a unit vector pointing in the direction of the incident ray and "'n "'is the unit normal to the surface, the direction "'r "'of the refracted ray is given by:
12.
In anisotropic media such as some crystals, birefringence may split the refracted ray into two rays, the " ordinary " or " o "-ray which follows Snell's law, and the other " extraordinary " or " e "-ray which may not be co-planar with the incident ray.
13.
Given a normalized light vector "'l "'( pointing from the light source toward the surface ) and a normalized plane normal vector "'n "', one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence \ theta _ 1 and angle of refraction \ theta _ 2, without explicitly using the sine values or any trigonometric functions or angles:
