There seems to be a limit, around 0.33, on the fastest possible aperture of a photographic lens made of glass. Is there a theoretical limit on the minimal focal length of a photographic lens (rectangular projection, not a fisheye)? Are the physical reasons that would prevent a, say, 1 mm focal length lens for a full frame sensor?

I also asked this question on Photography SE, but didn't get quite the answer I was looking for.