Simulating the Action Principle in Optics

Light has a fascinating property: it always travels the path that takes least time between any two points. This is motivating property behind optical phenomena such as reflection and refraction. The unreasonable economic efficiency of light captured by single proposition: principle action (PLA) in optics. Unlike refraction, which emerge from optimizing one-dimensional function, PLA emerges an infinite-dimensional functional. can be difficult for students to comprehend, formulation Lagrangian often left unexplained. To this end, paper presents various simulations demonstrate principle, including numerical solution generalization brachistochrone problem arbitrary refractive profile. interactive discussed are available at Ref. 1.