Caustics

The description of particular curves could go on for quite some time. Those who are interested can see on the computer some simulations of mechanisms to draw various types of curves. We will proceed with the visit and examine both the general structure of curves and the specific properties of some of them.

We have seen how conical sections, and in particular parabolas, have the ability to concentrate light rays in one point. Other curves do not, in general, have this property. This however does not mean that the reflected rays scatter completely, illuminating space more or less uniformly. Very often they concentrate not in a point, but on a curve: the caustic. Like the focus of conical sections, the name of this curve derives from "burning"; in fact, the term caustic means burning. In reality, the name does not correspond to an actual ability to light up a fire, at least as long as the light source has a low power, like a light bulb.

Caustics are often seen in everyday life, such as when a kitchen bowl is lit obliquely: the rays reflecting on the vertical side draw a curve on the bottom, which is called a reflection caustic, because it is obtained through the reflection of light rays.

Caustics can also be obtained through refraction, when the rays coming from a point penetrate a medium with varying density.