Interpretation of Fermat's Principle

Abstract

IN the wave theory of light, the geometrical laws of optics—rectilinear propagation, reflection and refraction—and other results besides, rest on a single principle. The fundamental postulate is that any train of waves may be replaced by a sheet of sources of suitable intensities and phases, that is, paths such as APCB of Fig. 1 of Mr. Darbyshire's letter are to be taken into consideration equally with paths like AQDB. Of all possible paths, the rays of geometrical optics are found to be stationary paths and so suitable for phase calculations; this is the essence of Fermat's Principle.