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  "body": "\n## Summary\n\nA caustic is the [[envelope|827KR3MVVY]] of a family of rays, the curve or surface where nearby rays focus.\nIn symplectic terms, project a [[Lagrangian submanifold|H8ACPTMX08]] of a cotangent bundle to the base.\nThe caustic is the set of critical values of this projection, that is, the image of the [[Lagrangian singularities|QKPMR9MC9W]].\nCaustics appear in optics as the bright curves of focused light.\nThey also appear in the asymptotics of oscillatory integrals and of short-wave solutions of wave equations.\nTheir generic local shapes, such as folds and cusps, are given by Arnold's classification of Lagrangian singularities.\n\n## Explanations\n\n### L1 human\n\nOn a sunny day the inside of a coffee cup shows a bright curve with a sharp point.\nLight rays reflected from the curved wall crowd together along this curve, so it is much brighter than its surroundings.\nThat bright curve is a caustic: the envelope that the reflected rays touch.\nA simple case from geometry is the family of normal lines of a plane curve, whose caustic is the [[evolute|Y3ZNV24V2C]] of the curve.\nFor a parabola the evolute has a cusp, and such cusps are the typical sharp points of caustics.\n",
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