Caustic (mathematics)

In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold.

It is related to the concept of caustics in geometric optics.

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.

[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

; the reflection of the direction vector is (normal needs special normalization) Having components of found reflected vector treat it as a tangent Using the simplest envelope form which may be unaesthetic, but

; i.e., light entering a parabolic mirror parallel to its axis is reflected through the focus.