Simulating the Action Principle in Optics

“Simulating the Action Principle in Optics”, published in The Physics Teacher on 02/23/23.

The job of a telescope is simple: to maximize the amount of light it captures. Indeed, light is the very phenomena which enables us to conduct astronomical observations, so it is worth studying the many different ways optical effects can manifest themselves in astronomy, from gravitational lensing to diffraction spikes. Indeed, light has a fascinating property: it always travels the path that takes the least time between any two points. This is the motivating property behind optical phenomena such as reflection and refraction. The unreasonable economic efficiency of light is captured by a single proposition: the principle of least action (PLA) in optics. Unlike reflection and refraction, which emerge from optimizing a one-dimensional function, the PLA emerges from optimizing an infinite-dimensional functional. To this end, this talk (and the associated paper) presents various simulations to demonstrate the action principle, including a numerical solution to a generalization of the brachistochrone problem to an arbitrary refractive profile. The interactive simulations discussed in the paper are available here.