Definition

Let S be a given curve and let F be a fixed point called the radiant point. If rays from F are reflected by the curve, the envelope of the reflected rays is called the caustic of S with F as radiant point. Expressing this geometrically, let any line through F meet the curve at Q and let QP be drawn so that QP and QF make equal angles with the tangent to the curve at Q; then the envelope of QP is the caustic.

This caustic by reflection is sometimes called the catacaustic, to distinguish it from a curve similarly formed (the diacaustic) when the rays are refracted. Diacaustics will not be discussed here and the word caustic will be used to mean the catacaustic.

The Drawing of Caustics

In general it is necessary to draw the normal (or the tangent) to the curve at Q. If the image of Fin the normal (or the tangent) is joined to Q, this is the line QP whose envelope is the caustic. If the curve S is a circle, however, use can be made of the fact that equal chords drawn from a point on the circumference are equally inclined to the radius.