In a room made of one way mirrors, may light be equally spread when shone from a single source from within?

Question

I know that there are a few existing questions about boxes lined with mirrors, but this is an interesting twist. Assume that when light hits a surface, precisely half of it is reflected and half of it escapes the box. The mirrors are lined up with as perfect exactitude as humanly possible - this means that it looks perfectly cubic to us, but, for instance, if you were to shine a torch with a linear beam at one wall it would not go straight back into the torch. Now, if you were to shine it into, say, one corner from the opposite corner, the light would go off in every direction, and bounce around interminably (that is, until the beam's intensity became infinitesimal from being halved so many times) - but would the torch, based in its own corner, end up with the same amount of lighting on it as the corner the beam is on?

Answer 1

Yes. The room would be bathed in a uniform density of photons from all the reflections.