Originally posted by RioRico You have to consider: what does f-stop mean, aperture-wise?
The f/number is a ratio of focal length to aperture opening. At f/2, the aperture is 1/2 the focal length. I'm holding a SuperTak 55/2; focal length is 55mm, aperture wide-open (f/2) is 27.5 mm; front lens diameter is about 33mm. To make that an f/1 (ignoring all necessary corrections), the rear lens and aperture would be 55mm, and the front lens would be correspondingly larger, as would the lens body. A slower lens, an Industar (Russian) 50/3.5, is little more than a pancake. Fast means fat.
Though I agree with your general assessment, your maths is simply not correct.
The open aperture is defined by the entrance pupil, not by the exit pupil. There is no reason, why the rear element of a 50/1.0 needs to be 55mm in diameter. Reality proofs that: The Noctilux would not fit into the M-bayonet if it where that size. According to your theory the rear element of a simple Pentax DA 200/2.8 would be more than 71mm in diameter - how is that supposed to fit the camera at all?
Originally posted by RioRico So, think about designing a fast long lens -- a prime, not a zoom. We'll make it a simple long lens, no fancy folded elements. We want a 300/1.5. The rear element needs to be 200mm across -- that is EIGHT INCHES!! The front element would probably be 250-300mm -- TEN TO TWELVE INCHES!! Even with aspherical plastic lens elements, that's gonna be one heavy, clumsy SOB. Make it a zoom, with distortion corrections at every focus, and it gets worse, much worse.
The reality is: a 300/2.0 would afford a 150mm diameter front lens! It may be a couple of millimeters bigger to allow for some image formation before the ray bundle goes through the iris (aperture), which would need to
provide the full 150mm diameter seen from the front.
I have set that in bold, because this is important: we are not talking about the mechanical dimension of the aperture, but about its projection, as viewed through the front lenses, aka the entrance pupil.
The diameter of the rear element is a totally different proposition, because it has not much to do with the question whether a lens is fast or slow. The diameter of the rear element plays mainly a role in vignetting and in illuminating a certain film/sensor format. Thus a lens for a medium format camera would need a bigger rear element, than one designed for 4/3 cameras. But that has nothing to do with the max. aperture!
Ben