How many times does the light reflect?

[Papatom]

My question is inspired by this thread:
https://www.physicsforums.com/threads/can-you-solve-this-geometry-problem-for-nine-year-olds.890794/

If you an isosceles triangle and you put in a corner (or somewhere else) a light beam (laser) the beam will reflect one or more times before it comes down to the base. See picture. Is there a general equation for how many times the light is reflected by the legs? Can you calculate from the angle and how many reflections there are how high the beam comes. It is evident that all beams must come down to the base again. Is there a proof for?

Triangle number 1 is the 9-years old question. If the angle of the laser with the base gets larger, the beam gets more and more reflected until it is reflected downwards again. Points A and C are the special cases were the beam is reflected back to the same corner.

Does anyone knows if there math available to calculate this?

 

[mfb]

At every reflection, the incoming angle (relative to the surface) is equal to the outgoing angle. That allows to set up a short equation how the angle (relative to the base, for example) changes with every reflection. Based on that it is possible to find a general formula.