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Wave Propagation and the Formation of Caustics

Antônio Sá Barreto

Purdue University

West Lafayette, IN 47907,

U.S.A

In this lecture we will discuss one example of a mathematical problem which arises in the theory of geometric optics. When light passes through, or is reflected by, a smooth surface, the image formed is in general a surface with singularities, that is, kinks or corners. These singularities are called caustics. There is a classical example of a cusp formed in a tea cup, which we hope we can demonstrate. We will state the general mathematical question, but we will concentrate our discussion on this particular example.

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