catacaustic

Catacaustic refers to the caustic curve formed by the envelope of light rays reflected from a curved surface. The term distinguishes reflection-caused caustics (catacaustics) from those formed by refraction (diacaustics). In geometrical optics, a catacaustic is the locus of points tangent to or intersected by the family of reflected rays from a given light source, and it depends on both the surface shape and the source position.

A classic example is a circular mirror. If the incident light consists of parallel rays (a distant source), the catacaustic is a nephroid, a two-cusped curve. If the light source lies on the circle, the resulting catacaustic is a cardioid, with a cusp at the source location. Other source positions and other reflective shapes yield a variety of caustic curves.

Catacaustics are observable in everyday life; the bright curves seen at the bottom of a coffee cup or inside a glass are familiar examples of reflection-caustics. They also arise in optical design and in the mathematical study of envelopes and singularities.

Historically, caustics have been analyzed since Huygens and were later named to distinguish the reflective (catacaustic) from refractive (diacaustic) cases. The study of catacaustics combines geometric optics with projective and differential geometry to describe how light concentrates along these curves.