ON CALCULATING THE OPTICAL PATH LENGTH IN SIMPLE SYSTEMS PART II,
The optical path length (OPL) refers to the product of the refraction coefficient of a substance and the path that light takes in going through the substance from the source to the detector. According to Fermat's principle, the OPL ought to be stationary. In addition to the Monte Carlo approach presented last year  based on the work of Gould and Tobochnik  that calculates the OPL for the refraction of a light ray traversing through two media with different refractive indices. Here, the study is extended to include a calculation of the OPL using the variational principle  to obtain an Euler equation for the OPL. For a two-layer media an analytic expression can be obtained that agrees with Snell's law. This concept is extended to more general media so as to solve the Euler equation numerically. The results of the Euler equation method are compared with the Monte Carlo calculations.  "A monte carlo calculation of the optical path length in simple systems," J. E. HasbunGeorgia Academy of Science annual meeting, V74, p48 (2017).  "An Introduction to Computer Simulation Methods" 2nd. Ed, H. Gould and J. Tobochnik (Addison Wesley, Reading MA, 1996)  "Mathematical Methods in the Physical Sciences," 2nd. Ed., M L. Boas (J. Wiley, NY, 1983).
Hasbun, Javier E.
"ON CALCULATING THE OPTICAL PATH LENGTH IN SIMPLE SYSTEMS PART II,,"
Georgia Journal of Science, Vol. 75, No. 1, Article 94.
Available at: https://digitalcommons.gaacademy.org/gjs/vol75/iss1/94