>>3620402Solely the optical design/formula of the lens.
Roughly I'd say the 2 biggest factors determining the optical formula are:
1. "Category" of optical design, i.e. symmetrical vs retrofocus, and their longer focal equivalents, symmetrical vs telephoto. In wideangles, a symmetrical lens will be on principle shorter than a retrofocal. On the longer focals, a symmetrical lens (long focus) will be on principle longer than a telephoto.
2. How well corrected you need your lens, from spherical+chromatic aberrations, and also geometric distortion. Here aperture plays a role, because apart from increasing the girth of a lens, it increases its physical length too, as you need more elements for the same level of correction compared to a slower lens. Same goes for retrofocals, for the "same" level of correction for geometric distortion especially, you need many more elements compared to a symmetrical design.
So in the end, say for wideangles at a given level of performance, say sharpness, all the following add physical length due to the need of more elements:
•retrofocal (which you're forced to do due to flange distance or mount size limitations)
•larger aperture
•lower distortion (for retrofocals mostly)
•lower vignetting (for symmetricals mostly)
You can test this in practice. According to the above, a sharp wideangle with a retrofocal design, fast aperture (say f/2.8) and low distortion will be relatively huge in physical length compared to its focal length.
Now check the 15mm f/2.8 Distagon.
And vice versa. A sharp wideangle with a symmetrical design, slow aperture, and no regards for vignetting, will be much smaller. Now check the 15mm (or 16mm) f/8 Hologon. Or the 21mm f/4.5 Biogon (though that is a hybrid design).
Last factor that can *reduce* the physical length of a lens, is use of aspherical elements. Aspherical elements can replace a larger number of spherical elements, for the same level of correction.
