Finding Snell’s Law as a Max-Min Problem Using Fermat’s Principle

Image: Rhett Allain

Let me be clear. My main goal is to get to the calculus of variations and use the Euler-Lagrange equation for some cool stuff. However, I think it’s important to start off with some problems that sort of do the same thing but are less complicated.

So, here is the situation. I want to find the path of light as it travels from one medium (say air) into…