Two Variations on the Periscope Theorem

    2020, Volume 25, Number 1, pp.  11-17

    Author(s): Tabachnikov S.

    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
    Citation: Tabachnikov S., Two Variations on the Periscope Theorem, Regular and Chaotic Dynamics, 2020, Volume 25, Number 1, pp. 11-17

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