Perhaps a light sensor? You are not going to use your mirror in a dark room. Unless you want the display to show up in the dark, but personally I wouldn't want that.
That wouldn't work during the day if your bathroom has a window (it'd be on all day).
I think the simplest way to do it would be to tie it in directly to your light switch. (Note that the light switch wouldn't be controlling power to the Android device, it would merely be a data signal determining whether the display should be on.)
Right, but you may not want the mirror to always be on just because you're standing out of it's viewing angle in the same room at 11PM when the moon is out. Maybe a combination of light and motion sensors..?
Motion sensing seems like a better solution to me. I can imagine looking from diagonally across the room wanting a quick glance at the current temp outside and it not showing up because it doesn't see my face.
Solid point. Maybe just a cheap wide angle lens from ebay and use easy off the shelf background subtraction from opencv at a low frequency as an easy of motion detection. I'm trying to think of ways to avoid integrating external peripherals that aren't part of the phone.