Mathematical retroreflectors

TL;DR

This paper introduces a collection of billiard-type retroreflectors, including three known asymptotically perfect designs and a new near-perfect design called the notched angle, with proofs of their retroreflectivity.

Contribution

The paper presents a new retroreflector design, the notched angle, and provides proofs of its retroreflectivity, expanding the set of known billiard-type retroreflectors.

Findings

Three objects are asymptotically perfect retroreflectors.

The fourth object, notched angle, is nearly perfect.

Proofs confirm the retroreflectivity of the new design.

Abstract

Retroreflectors are optical devices that reverse the direction of incident beams of light. Here we present a collection of billiard type retroreflectors consisting of four objects; three of them are asymptotically perfect retroreflectors, and the fourth one is a retroreflector which is very close to perfect. Three objects of the collection have recently been discovered and published or submitted for publication. The fourth object - notched angle - is a new one; a proof of its retroreflectivity is given.