English

The Ptolemy-Alhazen problem and spherical mirror reflection

Complex Variables 2018-01-23 v3

Abstract

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.

Cite

@article{arxiv.1706.06924,
  title  = {The Ptolemy-Alhazen problem and spherical mirror reflection},
  author = {Masayo Fujimura and Parisa Hariri and Marcelina Mocanu and Matti Vuorinen},
  journal= {arXiv preprint arXiv:1706.06924},
  year   = {2018}
}

Comments

20 pages, 5 figures

R2 v1 2026-06-22T20:25:18.455Z