In other words, does the size of projected image circle matters in the size and weight of two lenses with the same aperture/DOF (different f-number) and field of view (different mm)? All other things equal, will a 40mm F4 full-frame lens be identical in dimensions and weight to a 20mm F2 Micro 4/3 lens? Or bigger? Or smaller? Why?
My question is similar to "Does sensor size dictate lens size with all other things equal?" but there they only discussed lenses with equal f-number, where the smaller one can't make the same images as the the larger one wide open.
Does the f-number matters in that answer? Like, a 40mm F5.6 is the same size of a 20mm F2.8 but a 40mm F2.8 is smaller than a 40mm F1.4? I ask because a moderator here called jrista stated the following in a answer to the question Does the size of the front glass mean anything? :
once you pass f/2.8, each additional stop greatly increases the physical size of the lens. Additionally, once you pass f/2.8, each additional stop requires a considerably greater amount of light, and larger front lens elements are a key factor in gathering that additional light.
But I don't understand why F2.8 is such a "magical" turning point.
As a side question, the design of both lenses has to be totally different? Or is it just a matter of changing one or two glass elements at the base of the lens to adjust the projected image size? I ask that because one can transform a 40mm F4 lens into almost a 20mm F2 lens with a speed booster, but there are many downsides to that as it is extra glass. But if the manufacturer can make such minimal changes on the lenses avoiding those downsides, why I have never seen they release two versions of the same lens at the same time, one for APS-C and another for full-frame, like they do for different mounts?
Are different designs optimal for each focal length? Why?