Yet another way to derive Snell's law is based on translation symmetry considerations. For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the propagation vector k → → is proportional to the photon's momentum, the transverse propagation direction ( k x , k y , 0 ) must remain the same in both regions. Assume without loss of generality a plane of incidence in the z , x plane k x Region 1 = k x Region 2 . Using the well known dependence of the wavenumber on the refractive index of the medium, we derive Snell's law immediately.