When you shine a beam of red laser light on a piece of glass, it can bend in different ways. Here we present a few examples and show how to mathematically work through them using Snell's Law and geometry, rather than use thin-lense approximations.
Problem 1 - Light bends through a prism.
Problem 2 - Light goes into a prism, reflects inside, and then goes out at a completely different angle.
Problem 3 - Light bends through a plano-convex lens.
Problem 4 - Light bends through a plano-convex lens oriented the other way.