This article is cited in 2 papers

Special issue: In honor of Valery Kozlov for his 70th birthday

Two Variations on the Periscope Theorem

Serge Tabachnikov

Department of Mathematics, Penn State University, University Park, PA 16802, USA

Abstract: A (multidimensional) spherical periscope is a system of two ideal mirrors that reflect every ray of light emanating from some point back to this point. A spherical periscope defines a local diffeomorphism of the space of rays through this point, and we describe such diffeomorphisms. We also solve a similar problem for (multidimensional) reversed periscopes, the systems of two mirrors that reverse the direction of a parallel beam of light.

Keywords: periscope, optical reflection, projectively gradient vector field.

MSC: 78A05, 37D50

Received: 22.08.2019
Accepted: 24.12.2019

Language: English

DOI: 10.1134/S1560354720010037

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