English

Decartes' Perfect Lens

General Mathematics 2007-05-23 v4 Classical Analysis and ODEs

Abstract

We give a new, elementary, purely analytical development of \textsc{Descartes}' theorem that a smooth connected surface is a perfect focusing lens if and only if it is a connected subset of the ovoid obtained by revolving a cartesian oval around its axis of symmetry.

Cite

@article{arxiv.0704.1059,
  title  = {Decartes' Perfect Lens},
  author = {Mark B. Villarino},
  journal= {arXiv preprint arXiv:0704.1059},
  year   = {2007}
}

Comments

12 pages; proof of the exceptional cases to Drucker's theorem elaborated; one new importante reference is added; typos corrected