In differential geometry, differential topology, and singularity theory, a caustic is the critical value set of a Lagrangian mapping (? ? i) : L ? M ? B; where i : L ? M is a Lagrangian immersion of a Lagrangian submanifold L into a symplectic manifold M, and ? : M ? B is a Lagrangian fibration of the symplectic manifold M. The caustic is a subset of the Lagrangian fibration's base space B. One example of a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the optical concept of caustics. The ray's source may be a point (called the radiant) or infinity, in which case a direction vector must be specified.

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