Two Variations on the Periscope Theorem

Serge Tabachnikov

doi:10.1134/S1560354720010037

Two Variations on the Periscope Theorem

Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	11-17
Number of pages	7
Journal	Regular and Chaotic Dynamics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1134/S1560354720010037
State	Published - Jan 1 2020

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1134/S1560354720010037

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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.",

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AB - 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.

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Two Variations on the Periscope Theorem

Abstract

All Science Journal Classification (ASJC) codes

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