I think a more interesting question is how the rear view mirror works. What I mean is how does a perfectly clear image become slightly dimmer when you adjust the angle of the mirror? I've seen that since I was a child but I've never understood why it works.(I never got past calc based physics in college so if the answer is obvious I apologize.)
I'm assuming you're talking about what happens when you flip the manual "dimming" switch on the mirror.
I'm pretty sure you're looking into a mirror that actually has two reflections. One of them is already dim, and it's dominated by the brighter one so you don't normally see it. (Sometimes in the right light you can see both reflections at once.) The two reflections are offset, so that when the bright reflection is showing you the view out the rear window, the dim reflection is showing you a few degrees lower, probably the back seat. When you flip the dimming button, the mirror turns upward a few degrees, so that the dim reflection is now showing you the view out the rear window. You can't see the bright reflection any more because it's now showing you the roof inside the car, which is pretty dark in relation to the rear window. Now the "dim" reflection is actually bright enough to dominate.
I assume that this is accomplished with some sort of double mirror, where the "bright" mirror is closer to you, and some light leaks through it to hit the "dim" mirror behind. These could be made into a single unit with no actual space between them. It just needs two layers of reflective material that are at slightly different angles.
The bright reflection is the reflection off the silver backing of the glass in the mirror (i.e. the normal mirror reflection). The dim reflection is the reflection off the surface of the glass (the same as the reflection you see of yourself when you look at a window when it is dark outside and bright inside).
Flipping the "switch" on the mirror simple changes the angle of the mirror by the exact amount needed to reflect the light from your rear window into your eye off either the silver surface or the glass surface.
