Quote: "So what if you have a light source then surround it with a box(or sphere) made with a half-silver surface(half the light is reflected back inside, other half escapes). You stand on the outside, but then you and the box are surrounded in a perfect mirror box(or sphere). Would this then make it possible to see? "
Would it make it possible to see what? If the light source container was a sphere and the light source was a perfect point light(no radius) and it was in a perfect vacuum, then the majority of what you would see would be the light source, the light reflected from the 2 immediate mirrors exactly behind the light source(which would be virtually indistinguishable from the light source itself) as well as the parts of your body that have a line of sight to the light source. There would be a very faint reflection from the reflected and emitted light from your body too.
If your inner container was a box and/or your light source had a radius, then you would also see some illumination from surrounding points on both mirrors. But if it's the first scenario then the majority of the light would not be visible to you and would pretty much indefinitely bounce back and forth along a line. So if you left the light on for a while then moved, you'd find yourself severely burned as you come into contact with these areas. You'd also want to tie yourself to the side of the mirror so you don't slowly drift to the other side

.