Parabola Caustic with incoming light perpendicular to the axis

Download Geometry Expressions File

The caustic curve (or catacaustic) is the envelope of a family of reflected rays. If a set of rays parallel to the axis of a parabola is reflected in the parabola, they all pass through the focus, and thus the caustic is a single point. If set of rays perpendicular to the axis reflects in the parabola, the result is a cubic curve, called the Tchirnhausen cubic.

In the diagram, the caustic is shown both as an implicit cubic and as a parametric cubic.

Expressions

Name Input
Caustic Parametric Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Caustic Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image