TL;DR
This paper explores two types of multi-dimensional periscope systems with two mirrors, analyzing how they induce specific local diffeomorphisms of wave fronts, contributing to geometric optics understanding.
Contribution
It introduces and characterizes two variations of the periscope theorem, detailing the local diffeomorphisms induced by these mirror systems in multi-dimensional spaces.
Findings
Characterization of spherical and flat wave front transformations
Description of local diffeomorphisms induced by two-mirror systems
Extension of the periscope theorem to multi-dimensional settings
Abstract
A spherical periscope in multi-dimensional space is a system of two ideal mirrors that reflect the rays emanating from a fixed point to the rays coming back to the same point, and a reversed periscope is a system of two mirrors that reflect the rays having a fixed direction to the rays having the opposite direction. We describe the local diffeomorphisms of the wave fronts (spherical, in the former, and flat, in the latter cases), induced by these 2-mirror systems.
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