Caustics are bright patterns of light formed by the reflection or refraction of rays from curved surfaces. The author explains the history, mathematics, and physics of caustics, and provides some Python code to generate and visualize them.

The mathematics and physics of caustics are based on the Eikonal equation, which describes ray trajectories through optical systems. The Eikonal equation relates the optical path difference, which is the difference in distance travelled by two rays, to the angular deflection of the rays. The angular deflection depends on the shape and slope of
the refracting surface, which can be expressed as a potential function. The Eikonal equation can be written as a system of partial differential equations for the two orthogonal angular deflections.