Would it be possible to construct a box where all 6 sides on the inside were mirrors, so that if you opeded it in a bright room, closed it, and then opened it in a dark room, light would flood out?

I should imagine that the particles constructing the lid of the box would have to close the box at a speed greater than c. Otherwise the photon would escape before you had a chance of closing the box and trapping the light.

Mirrors do not have 100% reflectivity, so no. You can, however, build up a high intensity if you keep adding the light. It's usually done in 1-D only, called a power buildup cavity. If the reflectivity is high, the light can make many round trips in the cavity before it is lost, so the power inside the cavity is many times the input power.

I should imagine that the particles constructing the lid of the box would have to close the box at a speed greater than c. Otherwise the photon would escape before you had a chance of closing the box and trapping the light.

 

No, because light would be constantly entering the box, so it would be full at any given moment. Including the time when you shut the lid.

Unfortunately, I don't think that's how it works...

 

[Edit: Plus, even if it worked, and I'm not saying it would, when you opened the box, you would get a flash of light so fast that you couldn't see it anyway.]

Oh, alright.