Catacaustic of a Parabola - Tschirnhausen Cubic

A light source at infinite distance from the parabola produces parallel light rays (in yellow). The rays are reflected by the parabola. If the rays have more than one intersection point with the parabola, they are reflected at both points. The reflected rays and their continuations are shown in light blue. Definition: The envelope of the reflected rays by the parabola is called the catacaustic of the parabola (also caustic).
  • Drag the first slider - numberRays to change the number of light rays.
  • Drag the sliders - directrix and focus to change the parabola.
  • The catacaustic is a Tschirnhausen Cubic. Use the slider - coefficient to fit the Tschirnhausen Cubic onto the catacaustic for different parabolas.