Diacaustic

Diacaustic is the caustic formed by refracted light rays as they pass through a curved interface between two media. It is the counterpart of the catacaustic, which arises from reflected light. Where a catacaustic is the envelope of reflected rays, the diacaustic is the envelope of refracted rays governed by Snell's law.

To form a diacaustic, light from a source in one medium strikes a smooth, curved boundary separating the media. After refraction, the resulting family of rays is traced, and the envelope of these refracted rays—the points where neighboring rays are tangent to a common curve—defines the diacaustic. The exact shape depends on the geometry of the boundary, the positions and nature of the light source, and the refractive indices of the two media.

The diacaustic can exhibit various features, such as cusps or smooth curves, and its appearance changes with the source position (e.g., point source versus distant source) and index contrast. In simple configurations, the problem can be analyzed with geometric optics and differential geometry, sometimes yielding interesting and recognizable caustic curves as results of the refractive process.

Diacaustics are studied in optics, mathematical physics, and computer graphics because they reveal how light concentrates after refraction. They appear in practical contexts such as lens design, transparency effects in curved glass, and the analysis of light patterns through curved media.