Originally posted by pentaxus They double the focal length but don't change the diameter of the front element which changes the f/stop two stops. A 100mm lens with a 50mm front element is an 100/50=2, an f/2 lens. A 200mm lens that has a 50mm front element is 200/50=4. An f/4 lens.
While element size is a factor in determining the effective aperture of a simple lens - such as a single element or doublet lens - it's only part of the formula of a complex lens.
The actual size of the aperture diameter is a bigger factor in deciding light gathering - but again, that varies depending on the formula of the lens. Telephoto lenses employ their design to package more magnification and aperture in a smaller barrel than a simple long focus lens would deliver.
Take for instance the latest crop of super normal lenses. Today's Pentax D-FA 50mm 1.4 needs a 72mm filter size to surround its whopping front element of the 15 element total. The older FA 50mm 1.4 fits its front element inside a 49mm filter mount. Both are 1.4 lenses, but one has a much larger front diameter than the other - a more complex formula with more corrections offered by many more elements (15 vs. 7).
However, if you were to pull both lenses apart and measure the actual largest diameter the aperture mechanisms opened up to, I expect you'd find they'd be pretty close.