Snell’s law of refraction is a conservation law of optical momentum. In infinitesimal form, it leads directly to the Hamilton equations for geometrical optics. The latter guarantee that the transformation of optical phase space produced by propagation through a medium where the index of refraction is continuously differentiable, is canonical. Discontinuous‐index systems such as refracting surfaces must be treated through a complementary description to show that they are also canonical. They have recently been shown to factorize into two ‘‘root’’ transformations, each depending on the properties of a single medium, and each canonical. This factorization is applicable to reflection off curved mirrors as well.