Snell's law
Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
It is also of importance in some optimization problems. For example, a lifeguard running to save a drowning person in the ocean will take a path that follows Snell's law. If the lifeguard can run at speed $v_1$ on the beach, and swim at speed $v_2$ in the ocean, then the angle $\theta_1$ at which the lifeguard enters the ocean (the angle of incidence) and the angle $\theta_2$ at which the lifeguard swims towards the drowning person (the angle of refraction) satisfies Snell's law if he takes the shortest possible path: $$ \frac{\sin\theta_1}{v_1} = \frac{\sin\theta_2}{v_2}. $$
Insight: If Snell's law gives an undefined result (perhaps because of a domain error for $\sin^{-1}$), that means the light wouldn't be refracted, but reflected instead. In terms of optimization, this means that the given scenario is not optimal.