Concentration of light, especially sunlight, can burn. The word caustic, in fact, comes from the Greek καυστός, burnt, via the Latin causticus, burning.

A common situation where caustics are visible is when light shines on a drinking glass. The glass casts a shadow, but also produces a curved region of bright light. In ideal circumstances (including perfectly parallel rays, as if from a point source at infinity), a nephroid-shaped patch of light can be produced.^{[2]}^{[3]} Rippling caustics are commonly formed when light shines through waves on a body of water.

Another familiar caustic is the rainbow.^{[4]}^{[5]} Scattering of light by raindrops causes different wavelengths of light to be refracted into arcs of differing radius, producing the bow.

The planar, parallel-source-rays case: suppose the direction vector is $(a,b)$ and the mirror curve is parametrised as $(u(t),v(t))$. The normal vector at a point is $(-v'(t),u'(t))$; the reflection of the direction vector is (normal needs special normalization)

which may be unaesthetic, but $F=F_{t}=0$ gives a linear system in $(x,y)$ and so it is elementary to obtain a parametrisation of the catacaustic. Cramer's rule would serve.

Example

Let the direction vector be (0,1) and the mirror be $(t,t^{2}).$
Then