Question

Fun question that requires some knowledge of calculus of variations, thought I'd derive. (Fermat's principle, Snell's law)

Answer 1

Consider light passing from one medium with index of refraction \(n_1\) into another medium with index of refraction \(n_2\) (Will draw figure). Use Fermat's principle to minimize time, and derive the law of refraction: \(n_1 \sin \theta_1 = n_2 \sin \theta_2\)