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Society Investigating Mathematical Mind-Expanding Recreations

November 1997 Feature Presentation
Wave Propagation and the Formation of Caustics
Antônio Sá Barreto

Department of Mathematics
Purdue University
West Lafayette, IN 47907,

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.

  • History of the Problem
  • Problems
  • Some Tools to Solve the Problems
  • Solutions to the problems
  • The Maple Program
  • References


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