# The problem of camouflaging via mirror reflections

## TL;DR

This paper introduces a visibility index for mirror-shaped bodies in billiards and geometric optics, providing a lower bound based on volume and minimal radius, advancing understanding of near-invisible bodies.

## Contribution

It proposes a new visibility index and derives a lower estimate related to the body's volume and size, opening avenues for further research.

## Key findings

- Lower bound on the visibility index based on volume and radius
- Insight into near-invisible mirror bodies in geometric optics
- Foundation for future research on invisibility approximation

## Abstract

This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We introduce a {\it visibility index} of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate to this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.