Say that you have an empty transparent cube. Then you put a reflective sphere inside – the biggest possible one. And then the next biggest possible reflective sphere. Or 8 of them, or any number of them. And so on.
You may consider a supertasking to do it, or just say that this is your transparent cube, packed with distinct reflective spheres of different sizes. There is no room for another sphere inside, no matter how small it would be.
It is just as the mentioned supertasked packing had been done.
Now, you beam an ideal ray toward one of the cube’s outer square’s midpoint. It will just reflect from the biggest sphere. The angle of incidence may even vary, doesn’t matter.
Now you beam a ray in the direction of one of the cubes main diagonals – from outside toward the center. Will it:
- bounce back immediately after reaching the corner
- bounce back after some finite time
- exit at the opposite corner after some finite time
- exit somewhere else after some finite time
- never come out again
- This is an illegal or ill defined question
What say you?