Does the sensor size matters in the size and weight of an equivalent lens? Why?

Question

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?

Answer 1

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)?

So one lens is (say) a 20mm, f/2, 20 degree field of view and the other is a 40mm, f/4 20 degree field of view? The two lenses have the same field of view and same size entrance pupil (roughly, aperture). The 40mm lens must be longer if the designs are the same, but scaled.

From the perspective of optical design, the two are not equivalent. A 20 degree f/4 lens is much easier to design than a 20 degree f/2 lens, and the increase in aberrations from f/4 to f/2 (for some aberrations, this increase is 4^8, or 65,000 times) is much larger than the reduction in geometrical aberrations (exactly 2x) by scaling the focal length.

If the lenses are not allowed to touch the sensor, and must be shorter than some length, then the designs are in some way restricted. If, for example, the image clearance must be greater than 38mm, as for EF mount, then the 20mm design is far more difficult than the 40mm design because it is both a faster aperture, and also much more inverse-telephoto.

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?

There is no single, general answer to this question. Allow me to add some qualifiers.

1. The M4/3 lens has an image clearance > 16mm.
2. The FF lens is for Sony E or Leica M mount, with image clearance > 18mm.
3. The two lenses must have the same pictoral resolution (e.g. 20MP, though MP is an inappropriate unit for a lens).

Under these conditions, the M4/3 lens must be better corrected than the FF lens and thus should be a bit longer, but probably lighter. If you changed the apertures to, f/2.8 and f/5.6, the FF lens would probably be doable as a triplet or 4-element thing. The M4/3 lens might require 5 elements.

If you push things so that both are far from a diffraction limited regime, e.g. f/1 for M4/3 and f/2 for FF, the FF lens may become larger due to the clearance constraint. Or, more specifically, the ratio of the clearance constraint to the focal length.

As a side question, the design of both lenses has to be totally different?

They naturally want to be different, but they could just be scaled versions of each other with suboptimal performance for one or both designs.

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?

You can do that, Angenieux offers it for some cine lenses, e.g. this one. I leave it to you to find the price of this lens.

In general, the "rear convert" or "speedbooster" design space is more restricted than complete freedom to let the APS-C and FF lenses be the distinct designs they want to be. For that to work, the booster and lens must be independently corrected, and you have to hope that the sign of their aberrations are opposite, and magnitude about equal. Or, the booster must be diffraction limited. This is quite difficult to do while maintaining a compact overall design.

Edit to address a new question

In the first part I understood that lenses for smaller sensors will be shorter because the smaller focal range but maybe heavier because more glass is needed to correct the aberrations.

This is correct; scaling the focal design by 1/2 will make it half the length, adding a lens or two to clean up the performance won't double it.

But then in the second part you said the M4/3 lens should be a bit longer and probably lighter? Is it longer because it must employ a retrofocal design that the 40mm didn't needed?

Correct again -- consider the double gauss lens, which has historically been used for most 50mm SLR lenses, and quite a few of the 40mm f/2 and 40mm f/2.8 ones as well. The focal length is 50mm and the lens' rear element sits (about) 38mm from the image¹ - the principal plane is somewhere inside the lens.

In a telephoto lens, the prinncipal plane is generally in front of and outside of the lens. In an inverse-telephoto, it is generally outside of and behind the lens. In a "mild" retrofocus design it may still be inside the lens, but close to the back.

If you start with a double gauss-like design, the first step to improving its correction is to split (turn into 2) or compound (cement into a doublet) the rear group. Then the front, then do the rear again, repeat ad infinitum. This stretches the lens out, and you will run into the image clearance constraint and have to change to a retrofocus form. The retrofocus form is naturally longer than the very compact double gauss.

I said the M4/3 lens would probably be lighter because the manufactures tend to use lots of lighter materials in the mechanics of the lenses. Those are responsible for the bulk of the weight in a lens like this example.

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¹ EF mount has a flange distance of 44mm but this is measured to the larger flat surface, not the tip of the bayonette. Lenses such as the 85mm f/1.2 place elements as close as the tip of the bayonette, and thus the clearance requirement can be said to be 38mm.

Answer 2

But I don't understand why F2.8 is such a "magical" turning point.

There's not any such magical turning point in theory. But in practice many camera systems with different lens mount designs and even vastly different registration distances (or flange focal distances) tend to have near the same throat diameter. The throat diameter is the width of the hole in the middle of the ring to which an interchangeable lens attaches.

The reason throat diameter is a factor is because even if lenses only need entrance pupils (the aperture as seen through the front of the lens) smaller than that allowed by a lens with diameter just large enough to cover the hole in the front of the camera the lens will still be slightly larger in diameter than the throat diameter. The need for the diameter of the lens barrel, at least at the rear of the lens, to be larger than the throat diameter should be obvious.

For the typical throat diameters of most common SLR/DSLR and even some mirrorless systems, that minimum lens barrel diameter roughly corresponds to the diameter needed to make a normal zoom lens (a lens with focal length encompassing between about 0.65X to 1.5X the diagonal of the film format or digital sensor) with a maximum aperture somewhere around f/3.5 or f/4 at the wide end and about f/5.6 on the long end.

With wider angle lenses the angle of view is just as, if not more, important than the maximum aperture in determining the minimum size of the front element of a lens. But until one gets into ultra-wide angle or telephoto territory, a lot of typical lenses still need front elements about the same size as that of a lens barrel large enough to cover the throat opening of the cameras for which they're made. To get constant aperture f/2.8 zoom lenses in the same focal length range, the front elements need to be larger than the "minimum" lens barrel size, as determined by the throat diameter, of most SLR/DSLR/mirrorless camera systems.

That's one reason kit lenses tend to be 18-55 f/3.5-5.6 for Nikon, Canon, Sony, Pentax, etc. crop bodies. For an 18mm APS-C camera, the lens barrel needed to fit the mount is just large enough, after everything else that is needed is squeezed in there, for a front element that results in an 18mm f/3.5 entrance pupil as well as a 55mm f/5.6 entrance pupil. The same is the case with 70-300mm f/4-4.6 telephoto lenses. The front elements needed for such lenses can just fit in a lens with a barrel slightly larger than the throat diameters/flange rings of the most common interchangeable systems.

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?

Well, they don't have to be totally different. But a lens of the same focal length that projects a larger image circle than another lens of the same focal length must also take in a wider angle of view at the front of the lens. FF sensors have a diagonal about 43mm in length. APS-C sensors have a diagonal about 28mm in length. The middle 28mm of the image circle projected by a FF lens will be the same field of view as the full 28mm image circle projected by an APS-C lens with the same focal length. The parts of the image circle projected by the FF lens outside of the middle 28mm will be parts of the scene not captured by the front of the APS-C lens. This requires a larger front element for wider angle lenses. There's not much difference for telephoto lenses where the angles of view are much narrower and front element size is determined by the entrance pupil size needed for a particular f-number at that focal length.

This is why you see a lot of APS-C only narrow angle zoom lenses and very few telephoto APS-C only lenses. The ones you do see are generally 55-200mm or 55-250mm. These APS-C only lenses are able to provide the same angle of view for an APS-C sensor at 200-250mm that requires a 300-400mm lens for a FF camera. The size and weight savings there are based on the less powerful focal length needed to get the same field of view.

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?

For the most part, lenses released by manufacturers are not breaking very much new ground with regard to angles of view and maximum apertures. Instead, they're further refinements of earlier lens designs. To someone unfamiliar with past lens offerings and the different focal lengths needed to provide the same FoV on camera systems with differently sized sensors, the corresponding lens offerings for each format may not be obvious.

Take the typical 24-70mm f/2.8 zoom offered by most (if not all) major camera makers for their FF cameras. The APS-C "equivalent" in terms of angle of view would be a 17-50mm f/2.8. Quite a few makers offer both 24-70mm f/2.8 FF lenses and 17-50mm f/2.8 APS-C lenses that have very similar designs. Another typical very wide angle FF lens is 16-35mm. The APS-C "equivalent" is a 10-22mm. Plenty of manufacturers offer both such lens options. As the angles get wider the same f-number gets tougher and more expensive to maintain, so the 10-22mm APS-C only lenses tend to have smaller maximum apertures than the fastest 16-35mm lenses. On the other end of the focal length ranges, a 55-200mm APS-C lens gives about the same FoV as a 75/80-300 lens on a FF camera.