Equations of motion for rays in a Snell's law medium

The equations of motion for a ray in a Snell's law medium with a varying index of refraction are derived. A stratified medium is considered. Explicit expressions are given for the velocity and acceleration components of the ray. These are derived directly from Snell's law. It is further shown that the propagation of a ray can be modeled in terms of Newtonian-like equations of motion and that momentum is conserved along the interface. It is shown that Snell's law follows from this conservation law. Properties of the motion are studied and an example is given.