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The word is from the Greek for "burn" or "burning".
In optics, a caustic is a bundle of light rays. For example a caustic effect may be seen when light refracts or reflects through some refractive or reflective material, to create a more focussed, stronger light on the final location. Such amplification, especially of sunlight, can burn -- hence the name.
A common situation when caustics are visible is when some light points on glass. There is a shadow behind the glass, but also there is a stronger light spot. Nowadays, almost every advanced rendering system supports caustics. Some of them even support volumetric caustics. This is accomplished by raytracing the possible paths of the light beam through the glass, accounting for the refraction, reflection, etc.
Reference: Max Born and Emil Wolf, Optics.
A caustic substance is one that eats away or chemically burns other materials. Concentrated solutions of strong bases, such as the hydroxides of alkali metals and alkaline earth metals, are usually caustic. Caustic substances, such as drain cleaners, are harmful to living tissue.
Caustic is also an abbreviation for "caustic soda," a common name for sodium hydroxide (NaOH).
See also: caustic (mathematics).