$|AB|$ and $|BC|$ are mirror surfaces. The light beam starts from point A with $\beta$ angle to x axis as shown the picture below.
1) What is the condition of the system parameters to reach to point $B$ $(x_0,0)$ after reflections between mirrors?
2) What is the reach time that depends on $x_0,\beta,\alpha$ if the beam can reach point $B$?
Assumtions: Mirrors are perfect plane and there is no loss during reflections and the speed of light is $c$.