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SIMMER

Society Investigating Mathematical Mind-Expanding Recreations

November 1997 Feature Presentation
Wave Propagation and the Formation of Caustics
Antonio Sa Barreto

Department of Mathematics
Purdue University
West Lafayette, IN 47907,
U.S.A

sabarre@math.purdue.edu

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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