Optical Path, Phase, and Interference

A powerful tool in wave optics is the concept of optical path length, a notion usually introduced with Fermat's principle.1–3 The analysis of Fermat's principle requires the application of the calculus of variations and the concept of an extremum, ideas too advanced for beginning students. However, the concept has proven its usefulness in the analysis4 of interference experiments such as those of Michelson and Fabry-Perot. In this paper we shall show how optical path length can aid in the analysis of a modified two-slit Young experiment.