obviously whatever light happened to be in there when you closed the box would remain in the box, but since mirrors don't reflect 100% of the light that strikes them (some is absorbed by the glass and other materials making up the mirror) it would very quickly be converted into a tiny amount of heat energy. The mirror box, any air inside, and the air outside will eventually reach thermal equillibrium.
Wouldn't the mirrors reflect each other? I was just thinking about reflecting mirrors.....I have never done an experiment to see what happens with mirrors reflecting each other, but i would think there would be some pretty strange effects.
ever taken a video camera, and plugged the output into a tv and pointed the camera at the TV so that the camera displays to the TV a video of the TV?... what you get is a picture of a TV inside a TV inside a TV and so on. If you set the zoom just right and then wave your hand in front of the camera, these perturbations will ripple through the image and give rise to some pretty interesting effect and self sustaining feedback loops.
We had a 3 mirror medicine/bathroom cabinent at my house growing up and both the end mirrors opened inwards. When I was younger, I used to open the outer mirrors in, so the mirrors basically formed a triangle and I would stick my head in the center. There were dozens upon dozen of images of mirrors and myself, progressively getting smaller, quite psychedelic reflecting back on it. I never tried it while tripping though, not sure I could handle it.