caustic

In geometrical optics, a caustic is the envelope of light rays from a light source after reflection or refraction at a surface or curve. When a caustic is produced by reflection, it is called a catacaustic; when it results from refraction, it is called a diacaustic. The source may be at a finite distance, in which case the result is called a point-source caustic, or at an infinite distance, producing a solar caustic. The shape of the caustic depends both on the geometry of the reflecting or refracting surface and on the position of the light source. For a circular surface illuminated by a point source on the circle, the caustic is a cardioid; if the source is at infinity, it is a nephroid. Other shapes, such as logarithmic spirals and catenaries, are also possible depending on the configuration. The concept of a caustic was studied by Ehrenfried Walther von Tschirnhaus in 1681 and subsequently developed by Jacques Bernoulli and Philippe de La Hire. It has applications in instrumental optics, acoustics, and the physics of waves.