I'm not entirely clear on your box idea, perhaps a little diagram could shed some light? I gather you want the images infinitely repeating, but remember to picture it as an actual object.
------------------ mirror
o object
------------------ mirror
You have to be able to see one side of the mirror, yet when you look at the mirror, you are viewing the image on a 90 degree angle. If you have some small mirrors, practice to see what works. It's a lot easier to figure it out by playing around with some mirrors (any mirror will do), than to understand the theory.
But the repitition of images 'phenomenon' is a lot simpler to understand than it seems. Think of it in terms of light. Light reflects/absorbs off/into the object, the remaining colours reflecting to your eyes, which then processes it as an visible image. In the same way, this light reflects to the mirror, again, reflecting to your eyes. Some of the light from the object can again reflect from the mirror to the other mirror and to your eyes, and so on. Thus, you are not just seeing the original object, you are seeing the image from the first mirror, than the image from the second mirror, and also subsequent images reflected back and forth in the two mirrors. It's a simplistic explanation but basically it's how it works.
Glad I can be of help, it was a cool little effect that I felt made a great photo and would make a great art project.