In optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, a caustic or caustic network is the envelope

Envelope (mathematics)

In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point. Classically, a point on the envelope can be thought of as the intersection of two "adjacent" curves, meaning the limit of intersections of nearby curves...

 of light rays reflected

Reflection (physics)

Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

 or refracted

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 by a curved surface or object, or the projection

Projection (mathematics)

Generally speaking, in mathematics, a projection is a mapping of a set which is idempotent, which means that a projection is equal to its composition with itself. A projection may also refer to a mapping which has a left inverse. Bot notions are strongly related, as follows...

 of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent

Tangent

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

, defining a boundary of an envelope of rays as a curve of concentrated light. Therefore in the image to the right, the caustics can be the patches of light or their bright edges. These shapes often have cusp singularities

Cusp (singularity)

In the mathematical theory of singularities a cusp is a type of singular point of a curve. Cusps are local singularities in that they are not formed by self intersection points of the curve....

.

Such concentration of light, especially sunlight

Sunlight

Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...

, 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

Nephroid

The nephroid is a plane curve whose name means kidney-shaped Although the term nephroid was used to describe other curves, it was applied to the curve in this article by Proctor in 1878. This and the information below may be verified in Lockwood, pp...

-shaped patch of light can be produced. Rippling caustics are commonly formed when light shines through waves on a body of water.

Another familiar caustic is the rainbow

Rainbow

A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...

. Scattering of light by raindrops causes different wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s of light to be seen in arcs of differing radius. Each such arc is a directional caustic.
In computer graphics, most modern rendering systems support caustics. Some of them even support volumetric caustics. This is accomplished by raytracing the possible paths of the light beam through the glass, accounting for the refraction and reflection. Photon mapping

Photon mapping

In computer graphics, photon mapping is a two-pass global illumination algorithm developed by Henrik Wann Jensen that solves the rendering equation. Rays from the light source and rays from the camera are traced independently until some termination criterion is met, then they are connected in a...

 is one implementation of this. Some examples of 3D ray-traced caustics can be found here.

See also

• Focus (optics)
  Focus (optics)
  In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
  
  
• Circle of confusion
  Circle of confusion
  In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source...
  
  
• Caustic (mathematics)
  Caustic (mathematics)
  In differential geometry and geometric optics, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the optical concept of caustics...