The
vector form of
Snell-
Descartes's law is
n2u2 - n1u1 = aN
where bold denotes vector quantities; n1 and n2 are, respectively, the index of refraction in the medium of incidence and in the medium of refraction; u1 and u2 are, respectively, unitary vectors along the direction of propagation in the medium of incidence and the medium of refraction; a is a proportionality constant; and N is a unitary vector normal to the interface between the media.
This only means that the incident and refracted rays are colinear with normal vector N.