One way to arrive at Snell’s law of refraction is to assume, as Pierre de Fermat did nearly four centuries ago, that light rays travel the fastest path between two points. If the points lie on opposing sides of the interface between optically different materials, then that path likely isn’t a straight line.
Richard Feynman likened the problem to that of a lifeguard—presumably a faster runner than swimmer—tasked with rescuing a drowning swimmer. The astute lifeguard, rather than make a beeline to the swimmer, would run toward a point on the shoreline that extends the length of the run in exchange for shortening the length of the swim. Likewise, when a light ray passes from a medium with a low refractive index ni to one with a high refractive index nt, its angle of incidence θi is larger than its angle of refraction θt,...
