Reading these last few posts reminds me of how surprised I am that my 135/2 isn't larger, especially compared with my 200/2.8
135 / 2.0 = 67.5
200 / 2.8 = 71.4
Only 4mm different...
Yes now you mention it I can see that based on the same maths the 200/2 and the 300/2.8 are similar diameter.
But if the formula is as simple as focal length / f stop, why does my 135/2 vignette much more at f2 than my 200/2.8 does at 2.8 ?
The simple formula is just that.. simple and a guideline. A lot more goes on in the world that is precision optics that can produce(or not) the vignetting you're experiencing.
Just to be specific, the relative aperture as a ratio couldn't be called a "guideline". It is a mathematical fact. The "entrance pupil" diameter, which is the diameter of the aperture as viewed through the front of the lens at "infinity distance", quite literally IS the focal length divided by the relative aperture number. There is no guideline here, that is quite specifically EXACTLY how to compute the size of the entrance pupil, which puts a limit on the minimum size the front element can possibly be. If the front element were smaller than that, then the entrance pupil would have to be smaller as well.
Sometimes manufacturers "fudge" the design a little. For example, the 100-400mm L lens is actually more like 390mm, and the entrance pupil and the diameter of the front element are just a little smaller than would actually be necessary for a lens that was truly 400mm long (I've actually measured it myself.) For a ~390mm focal length, the numbers add up and seem to be correct, probably because it was a matter of manufacturability vs. cost to shorten the lens just a little. Not that it matters much, a few mm difference in focal length aren't going to matter (less than 5% difference in subject size relative to the frame), but it could mean quite a bit from a cost standpoint.
The size of the front element of a lens cannot be smaller than the entrance pupil, however it can be larger. I guess you could say it is a "guideline" that the front element has to be at least as large as the entrance pupil. Wide angle lenses tend to have front elements that are significantly larger than their entrance pupils, less so because of the needed light gathering power and more so just so they can gather incident light from an appropriately wide angle. In my 16-35mm f/2.8 L lens, for example, the front element is HUGE, while the aperture is quite tiny in comparison. I'd say the front element is dozens of times larger in area than the entrance pupil, maybe a dozen times larger in diameter.