If anyone happens to have an old projection tv laying around, the couple tv's I have taken apart over the years all used large first/front surface mirrors to reflect the projected image horizontally onto the back of the tv screen. I carefully cut up one of those mirrors a couple years ago (using glass cutters to make the cuts and my foredom tool to smooth up the sharp edges a bit). I made 5-6 slide in replacement mirrors for my Proto J2373 inspection mirror, so the mirrored glass can be easily replaced after it gets scratched up.
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That Proto is probably too large of a mirror for the OP, but with a little patience one could probably make small round mirrors as well, to glue into place for smaller dental style mirrors.
I have also seen small (often long and narrow but they are still good quality) first surface mirrors inside computer printer/scanners. If you happen to have an old one laying around, it might be worth taking it apart to see if yours has a useful mirror in it.