I originally thought of this scenario many years ago, one night, when I had smoked too much (?) pot.
Around the same time I also decided to question the conventional wisdom that two mirrors, facing each other, was infinity. I had taken some physics books out of the library - one of which made that claim. I had an epiphany that it was not infinity. Here is why: what you are seeing when you place two mirrors face to face, (wrongly) assuming you could even make them perfectly aligned in such a manner, is nothing more than light bouncing from one to the other. Because light is traveling so quickly, there is instantly over a billion reflections (the precise number of reflections would depend on how far apart the mirrors happen to be). I actually took the time to calculate how many reflections would exist in 1 second if the mirrors were exactly 1 foot apart. It was over 1 billion reflections. So, although that is quite a large number, it is not infinity - nor would it ever be infinity unless time is infinite (in which case, nothing is not infinity - but then we start to get into the area of physics which is much more like mushrooms and less so like pot).
And recall, this assumes that the mirrors are in perfect alignment, which would be impossible to attain. Even the smallest misalignment would result in the eventual end of reflection. Much like two lines, if not perfectly perpendicular will eventually meet at one end, and drift further apart at the other.
