caustic curve
A curve to which the ray of light, reflected or refracted by another curve, are tangents, the reflecting or refracting curve and the luminous point being in one plane.
caustic curve: envelope of reflected or refracted light rays
A caustic curve is the path traced by the concentration of light rays after they have been reflected or refracted by a curved optical surface. When parallel rays or rays from a point source strike a mirror or lens, they do not converge to a single point but instead form an envelope, a smooth curve to which each reflected or refracted ray is tangent. This envelope is the caustic. You see caustics in everyday life: the curved patterns of light on the bottom of a swimming pool, the bright curves inside a coffee cup, or the sharp lines formed by sunlight through a wine glass.
Caustics arise from the imperfect focusing properties of curved surfaces. A parabolic mirror will focus parallel rays accurately at a single point, but a spherical mirror, which is cheaper and simpler to manufacture, focuses different rays at slightly different distances from the surface. These focal variations create a caustic curve that lies somewhere between the mirror and the intended focal point. The mathematical shape of this caustic depends on the geometry of the reflecting surface and the direction and intensity of the incoming light.
Variants and occurrence
Caustics occur with both reflection and refraction. A diacaustic is produced by refracted rays passing through a curved boundary between two media of different refractive indices. A catacaustic results from reflected rays bouncing off a curved mirror. In imaging systems, caustics represent a form of aberration; they limit the sharpness of the image and are often unwanted. Optical designers work to minimize caustics by using aspherical lenses and mirrors, which bend light more uniformly across their surface.
The term comes from the Greek kaustikos, meaning burning, because early observers noticed that caustics could concentrate light intensely enough to ignite dry materials. The caustic in a circular mirror or lens is sometimes bright enough to burn skin or paper if the light source is strong. In precision optics, caustics are measured and mapped to understand the quality of a lens or mirror and to correct for their effects in high-resolution imaging applications.