MathDB

You are given a

2021 \times 2021

square, its inner border is a mirror.

2020

of its squares have mirror borders, and all other squares have transparent borders. You are given an angle

\alpha \in (0^\circ, 90^\circ)

. A ray of light passes without change of direction through the transparent boundary, and is reflected according to the law of reflection when hitting the mirror boundary (if the ray hits exactly the corner of the mirror square, it is reflected from the horizontal side of the square, see the figure below for examples).
https://i.ibb.co/mqmTdNS/2021-UMO-8-6.png Prove that from some point on the bottom side of the square you can release a ray of light forming the chosen angle

\alpha

with this side (there are two such rays) so that the light reaches the top side of the square.
Proposed by Arsenii Nikolaiev

Problem Statement