CAUSTIC, CATACAUSTIC, and DIACACSTIC. In optics, C. is the name given to the curved line formed by the ultimate intersections of a system of rays reflected or refracted from a reflecting or refracting surface, when the reflection or refraction is inaccurate. When the C. curve is formed by reflection, it is called the catacaustic—somethnes simply the C.; when formed by refraction, it is called the diacaustic curve. In mathematical language, a curve formed by the ultimate intersections of a system of lines drawn according to a given law is called the enrelope, and is such that the lines are all tangents to it. As in a system of rays reflected or refracted by the same surface all follow the same law, it follows that the C. is the envelope of reflected or refracted rays.
An example of the catacaustic is given in the annexed figure for the case of rays falling directly on a concave spherical mirror, BAB', from a point so distant as to be practically parallel The curve may be said to be made up of an infinite number of points, such as C, where two very near rays, such as P, Q, intersect after reflection This catacaustic is an epicycloid. The curve varies, of course, with the nature of the
ease represented in the figure, the cusp point is at F, the simple example can be given of the diacaustic curve as that above given of the catacaustic. It is only in the sum .
Vest cases that the curve takes a recognizable form. In the case of refraction at a plane surface, it is shown that the diacaustic curve is the evolute either of the hyperbola or ellipse, according as the p-fractive index of the medium is greater or less than unity.
The reader may see a catacaustic on the surface of tea in a tea-cup about half full, by holding the circu lar rim to the sun's light. The space within the caustic curve is all brighter than that without, as it clearly should be, as all the 'light reflected affects that space, while no point without the curve is affected :pace, _ _ _ _ by more than the light reflected from half of the surface.