I have the following problem: a light beam enters a mirror room with integer coordinates in the plane (consider it as a polygon). One of the walls of the room is removed and a light beam enters the room. The initial (not reflected) beam is defined by two points with integer coordinates. It enters the rooms, reflects a number of times and exits the room. The goal is to maximize the ratio (number of reflections) / (number of sides of the room).
All coordinates should be in the range [0; 50].
Can you give me any hints or references to previous work on this problem. Thanks in advance!