focus a camera through or on a mirror?

In the middle of a brief intro to computer animation today we got off on a tangent that I probably would have completely dismissed had I not debated the same technical issue myself, many years ago. The idea is that if you point a camera into a mirror, is not everything in the mirror on one surface and therefore all at one focal distance? If so, then you can establish a mirror fixed to the front of a camera at a 45 degree angle and just shoot with the camera seeing the reflection. Some rudimentary physics tells us that this is not so. We do not look at the mirror, we look at waves bouncing off the mirror. I don't have the right vocabulary to describe it, but even if I did, math and science words are not convincing if you have no training in them. Instead, I solicited a mirror from the group (one girl had a 2 inch mirror) and I shot a pair of photos, one focused on the mirror (as seen by the frame of the mirror being in focus) and the other of the reflection (noting now that the mirror frame is no longer in focus). Tangible testing. We eventually returned to the computer demo.