Originally Posted by LeviticusMky

I would think that the amount of light that the flashlight emits would envelope the entire chamber, leving you in a perfectly white (or yellow or whatever the flashlight color is) chamber. As the mirror is a "perfect" one, the light would never stop bouncing, and as such it would overwrite any previous light information that was coming into your eye.

Possibly, if you had a flashlight that was strong enough, it could easily blind you, as the amount of light energy being added into the chamber would have nowhere to go, and would compound itself.

The only way that you could be assured that the light wouldn't fill the chamber almost immediately would be to do one of two things:
a)hold the flashlight PERFECTLY vertical/horizontal to the sphere along a diameter. This would result in a ring of light at the sphere's circumference.
b)hold the flashlight PERFECTLY still at the center point of the sphere, and point it directly out at any side. This would result in a dot.

I'm no physicist, or mathematician, so I may be wrong, but I'm usually not far off. I like to think things like this through...