Can a lens exist with an f-stop of less than 1? [duplicate]

As I understand it, the F-number of a lens is equal to the aperture diameter divided by the focal length. So f/1 would mean that the aperture is as wide as the lens is long.

Question: Is it physically possible for the aperture to somehow be wider than that? For example, something like an f/0.5 lens?

I gather that F-number is already the number one cause of expensive lenses, so even if such a lens is physically possible, it's likely to be far to expensive to actually buy. (To say nothing about whether it's even useful in the first place.) I'm just curious about the physics of the matter.

• Less interested in whether there's one for sale, more just "is it physically possible?" And apparently it is... – MathematicalOrchid Feb 25 '16 at 13:26
• "So f/1 would mean that the aperture is as wide as the lens is long." The focal length is not the same as the length of a lens. – osullic Feb 25 '16 at 14:02
• I had an f/0.85 C-mount lens in a previous job. I tried it on my Canon 350D but of course I had no infinity focus and lost the corners to vignetting. But they exist. – Chris H Feb 25 '16 at 16:42