Generally spoken, a caustic 1) is
formed by an envelope of light rays from a point source, diverted by some
optical instrument. The source can be at finite distance (like a flame) or at
infinite distance (like the sun).
Caustic qualities have been studied by Tschirnhausen (1682), Jacques Bernoulli (1691), and La Hire (1703).
The catacaustic of the logarithmic spiral is the curve itself (with a light source in the asymptote of the spiral). For a cycloid this is half true: for a cycloid arch, rays perpendicular to the x-axis result in two cycloid arches.
Some other catacaustic curves are:
The caustic can be generalized for different refraction indices (n1,
n2) at the two sides (same and opposite side of S, in relation to the
tangent). This curve is called the anticaustic.
anticaustic curves are the following:
The anticaustic curves have been studied by Mannheim.
1) Kaustikos (Gr.) = what burns..