understanding "fastness"

[Lee Jay]

If we take a lens like the 70-200/2.8, then you will see that as you change the focal length, the size of the entrance pupil will change in proportion to the the focal length, even though the front element stays the same. This shows you that for a typical zoom design, it is the desired f-number at the longest focal length that determines the minimum size of the front element.

I've wondered about this before. For the constant aperture zoom lenses, based on their physical design, could they also be made to be a variable aperture lens with a larger aperture on the short end of the range (or should I say, lower F number)? For example, with the 70-200 f2.8, at 200mm the entrance pupil has to be ~71.4 mm. If you took this same entrance pupil size with the focal length at 70mm, couldn't the lens max aperture be ~f1.0? So does the lens maker limit how much the entrance pupil opens based on the focal length? Or am I missing something (does it also have to do with the front element size?)?

So, the actual physical opening doesn't change. What changes is the apparent size of that opening when seen from the front of the lens. In essence, the front lens elements (those in front of the physical aperture) cause variable optical magnification of the aperture as focal length changes.

 

[chromophore]

If we take a lens like the 70-200/2.8, then you will see that as you change the focal length, the size of the entrance pupil will change in proportion to the the focal length, even though the front element stays the same. This shows you that for a typical zoom design, it is the desired f-number at the longest focal length that determines the minimum size of the front element.

I've wondered about this before. For the constant aperture zoom lenses, based on their physical design, could they also be made to be a variable aperture lens with a larger aperture on the short end of the range (or should I say, lower F number)? For example, with the 70-200 f2.8, at 200mm the entrance pupil has to be ~71.4 mm. If you took this same entrance pupil size with the focal length at 70mm, couldn't the lens max aperture be ~f1.0? So does the lens maker limit how much the entrance pupil opens based on the focal length? Or am I missing something (does it also have to do with the front element size?)?

That's a good question.

The thing to remember about lenses is that their optical properties are inseparable from their physical design. You can't take a constant-aperture zoom and somehow convert it into a variable-aperture zoom without having to change the entire lens formula--at which point, it would be a completely different lens.

To put it another way: it is tempting, but incorrect, to think of a constant-aperture zoom as somehow "wasting" some underlying ability of the design to achieve a faster f-number at the short end of the focal length range. Although the front element diameter may be determined by the requirements of entrance pupil size at the longest focal length, this is just one constraint among many when considering the design parameters. Could you make the lens smaller, lighter, or more cheaply if you sacrificed a constant-aperture constraint? Probably. But that's a different consideration. Conversely, if you were to attempt to design a lens that was variable aperture f/?? to f/2.8, that lens would be considerably more expensive than a constant aperture f/2.8. There's no free lunch, sadly.

The primary drivers of cost/difficulty of manufacture in a photographic lens are the fastest f-number of the design, whether the design is varifocal (zoom), the extent of deviation from symmetry (i.e., retrofocus or super-telephoto), correction for higher-order aberrations (in particular wavelength dependent aberrations), and the total number of interfaces (glass-to-air or glass-to-glass). Some of these are correlated factors, and in isolation, may not be too unreasonable to achieve, but various combinations can become extremely difficult to produce.