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