A couple points I want to make here.
Zerost (Zerst? Zeroist? 0*ist?): Guys, optics are confusing. This post involve way more rabbit holes than I thought it would. Still not sure I've got it all right.
First, almost all stated f/ numbers are approximations in one way or another. For example,
this f/4.5 lens is really f/4.6, and
this f/2.8 lens is really f/2.9-3.0.
Second, while we like to refer to f/stop being defined by a physical property (the aperture opening), it's a little more nuanced than that. It is defined by the focal length divided by the entrance pupil (
source; I know it's wikipedia, but the source is an optics textbook). This pupil, as bdery said, is a projected opening, not a physical opening. If there were no lenses bending the light between the thing you were taking a picture of and the aperture assembly (like a pinhole camera), they would be the same (
source).
This MIT lecture gives a slightly different definition for f/# calculation;
this OSU presentation shows the math on how they are equivalent. Also note that the field stop, which defines the field of view of the lens, is normally placed within the optics near the rear of the lens (but not always). My guess is that telephoto and retrophoto designs make what sounds simple—the location of the various stops and pupils—and makes it totally counterintuitive. Because complex engineering always does that.
I'd love to hear from a real optical engineer to see if I've got this all correct or if I'm way off course.
And finally, some
lens design humor.
Further reading:
photozone's series on lens design
Edit: The calculations for the nerd-level of the author of this post is left as an exercise for the reader.