Bodies with mirror surface invisible from two points

TL;DR

This paper demonstrates the theoretical possibility of constructing a mirror-surfaced body that remains invisible from two specific points by analyzing billiard dynamics and geometric optics principles.

Contribution

It introduces a novel construction of bodies with mirror surfaces that are invisible from two points, expanding the understanding of billiard invisibility in geometric optics.

Findings

Bodies with mirror surfaces can be designed to be invisible from two points.

The construction relies on specific billiard dynamics and geometric optics principles.

This work extends previous invisibility results to two-point invisibility scenarios.

Abstract

Here we are concerned with a special issue of billiard invisibility, where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is identified with the dynamics of light rays outside the body in the framework of geometric optics. We show that in this setting it is possible to construct a body invisible from two points.