They're called head mirrors (http://en.wikipedia.org/wiki/Head_mirror), believe it or not. =) The Wiki article has a little info, but if you do a Google search on "head mirror doctor" and so on, you might be able to find more in depth info that you're looking for.
I used to wonder about that too. Eventually I either found out (though I never knew what they were called) or worked it out based on the fact that there's a hole in the middle.
the sad thing is, I only learned about how these things work because they were a special drop in a game and it was called the "Otolaryngologist's mirror" in it.
ENT Doctor's mirror. Used to see inside dark places. :V
My husband swears that one was called a speculum, but we can't find a citation for that. Speculum is Latin for "little mirror" so he's probably right. Will get back to you with a reference after the breakfast dishes are tidied.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1125652/
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Well, damn.
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DIS A POINT:
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MAYBE I R A POINT U EVER THINK OF THAT HUH
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ENT Doctor's mirror. Used to see inside dark places. :V
It's a pretty clever piece of technology imo.
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BTW, you ask awesome questions.