The Ptolemy-Alhazen problem and spherical mirror reflection. (English) Zbl 1419.30005
Summary: An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically, this reduces to the solution of a quartic equation, which we solve and analyze using a symbolic computation software. Similar problems have been recently studied in connection with ray-tracing, catadioptric optics, scattering of electromagnetic waves, and mathematical billiards, but we were led to this problem in our study of the so-called triangular ratio metric.
MSC:
| 30C20 | Conformal mappings of special domains |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 51M99 | Real and complex geometry |
Software:
Risa/AsirReferences:
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