Parabola Caustic with incoming light perpendicular to the axis

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 |
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