Does sensor size dictate lens size with all other things equal?

Question

Background

I'm considering switching from DSLR to mirrorless and have been researching the micro four thirds (M43/MFT) and Sony's new Alpha 7 (A7). While Sony hasn't released many lenses for this new system, many are saying the lenses will be much larger and heavier due to the sensor being larger than MFT, despite the Sony being the same size as popular MFT cameras (Olympus OM-D E-M1). Lens size and weight is important to me since I'm wanting roughly APS-C quality or better in a much more portable system.

Question

How are people making the assumption that the full frame sensor of the Sony A7 will net larger heavier lenses to be equivalent to MFT versions? Does this pertain to width, length, or both? Would it be possible for Sony to eventually release smaller lenses similar to the Olympus MFT system without cropping the full frame sensor?

Answer 1

All other things being equal, yes.

There are two primary reasons why this is so.

• To maintain the same amount of field intensity of light over a larger area, a lens used with a larger sensor has to be able to collect more total light than a lens used with a smaller sensor. This means a larger entrance pupil, which usually works out to require a larger front element.

• The larger the sensor, the longer the focal length of a lens needs to be to give the same Field of View (FoV), and the larger an image circle it needs to project. On a compact camera with a small 1/1.6" sensor, a 50mm lens gives the same FoV as a 215mm telephoto lens does on a 35mm film camera. On an APS-C camera, a 50mm lens results in an FoV that is in the beginning of the telephoto range for a 35mm camera, 75-80mm. On a 35mm camera a 50mm lens is considered normal, because the focal length is very near the registration distance of the camera and because that focal length is roughly equal to the diagonal measurement of the plane that records the image. A medium format camera will give an FoV using a 50mm lens that is about equal to a 32mm lens paired with a 35mm camera. On a Large format 4X5 camera a 50mm lens gives an FoV about equal to a 13mm lens on a 35mm camera.
  a) Especially with longer focal lengths, the physics involved are hard to overcome. Although the strict technical definition of a telephoto lens is one that is designed so that the distance from the image plane to the front of the lens is shorter than the focal length of the lens, there is only so much one can do in reducing the size of a lens with a long focal length. This is especially true if the cost to produce such a lens is considered.
  b) Just as a 50mm lens used on a 4x5 camera must project a light circle considerably larger than the light circle cast by a 50mm lens designed for a 35mm camera, lenses designed for smaller sensors can project smaller light circles. This allows the lenses to be smaller in diameter. It also allows them to be made with less quantities of some of the most expensive materials used in a lens: the corrector element at the rear of the front group.

So a 50mm lens designed for a small compact can be both shorter and smaller in diameter than a 215mm lens that gives the same FoV on a 35mm camera. Even in terms of Micro Four-Thirds sized sensors, only a 100mm lens that throws a light circle slightly larger than 22mm is needed to provide the same FoV as a 200mm lens throwing a light circle at least 44mm in diameter on a full frame camera. An APS-C camera would need a 125-133mm lens with a 27-29mm light circle, depending on whether it is a Canon APS-C or Nikon/Pentax/Samsung/Sony.

Answer 2

The size of a lens is governed by the complexity of the design and the amount of light that needs to pass through it. For a given focal length with a cropped sensor, the amount of information that has to be brought in to the lens to produce the image circle can be much smaller because the entire full frame image circle doesn't have to be filled. If you are only using 60% of the sensor space, you only need 60% of the image circle and only need about 46% of the lens glass.

This is why a point and shoot can have a lens that is the equivalent of a 19mm to 450mm lens with a fairly quick aperture and only take up an inch or two where as the full frame DSLR version would take over a foot and a be bigger around than the point and shoot camera body is. It only needs to be able to resolve a very thin slice of the middle of the image circle that the full frame lens would have to be able to resolve. This means simpler, lighter, smaller and cheaper lenses, but it also means greatly reduced quality as diffraction plays a bigger role and the traditional sensor size issues all come to bear.

There are technologies like difractive optics that could reduce the sizes some, but that adds complexity and cost in exchange for size. It isn't possible to say that they won't ever make smaller lenses, but there is a good reason why the lenses are bigger and why the larger sensor size and slightly larger lenses are worth the size and cost if you are looking for the best quality you can get.

Answer 3

I thought it might be interesting to list some of the ways that things could not be equal (i.e. what would, in general, make a lens larger -- even if it was for a camera with the same sensor size).

Consider a fairly simple lens -- one for an old view camera. The lens itself may be physically small, even if it has a focal length somewhere between 150mm and 210mm. It has no automatic aperture, no fancy mount, no focusing mechanism, etc.

Now add a simple helicoid focusing mechanism, automatic aperture mechanism (stops down to shooting aperture before taking a picture), large diameter mount (with mechanical means of communicating aperture settings), unsimple focusing mechanism (the need to move different lens elements at different rates while focusing), electronic contacts to communicate between camera and lens (sometimes in addition to existing mechanical connections), autofocus motors and electronics. Other factors may include things like a desire on the part of the maker of the lens to allow for a common filter size across several lenses (which would affect the barrel size).

All of the above are why a Leica 50mm 1.4 lens might be a little smaller and lighter than a Nikon 50mm 1.4 lens, even if both are designed for the same size sensor.

Answer 4

Does sensor size dictate lens size with all other things equal?

The problem with your question is, when comparing full frame DSLR to micro four thirds, all else is not equal.

In this case the difference is not just the sensor size, but the lack of flip-up mirror, which really does have a significant effect on lens design and how big lenses can be.

In particular, the lack of flip-up mirror means the lens can be mounted much closer to the sensor, and this alone means that some lenses, particularly zooms or wide-angle lenses, can be made much smaller and simpler.

So there are a few different aspects to your question.

• As you would expect, if all else were equal, a smaller sensor would mean a lens of the same characteristics (focal length and aperture) would be smaller, in scaling with the sensor.

  This should be obvious when you think about compact cameras and cellphone cameras: they still manage the same angle of view and f-numbers like f/2.2 or so, but their lens assemblies are much smaller.

  Everything scales down nicely. Say you have a 50mm lens with a f/2.0 aperture on full frame DSLR. If you halve the sensor dimensions you get exactly the same f-number and angle of view with a 25mm focal length lens with half the lens diameter. f-number is already relative to focal length so an f/2.0 at 50mm is twice the diameter of a f/2.0 at 25mm already. So everything equally gets smaller as you'd expect.

  Because of physics, the weight of the lens actually scales exponentially with the diameter. For a start, the area of a lens will scale with the square of its diameter - but in addition the thickness of the lens can decrease too so it's actually approaching a cubic relationship. So a decrease in sensor size will result in an even bigger decrease in camera weight.

• But in the case of comparing DSLR and mirrorless, you get the added benefit of not needing a flip-up mirror assembly between the lens and sensor, meaning that the lenses can be mounted closer to the sensor. This allows wide-angle and zoom lenses to be made smaller and simpler for equivalent specs.

  To get more technical, lenses which are wide-angle, or zoom lenses which have a wide-angle end, need to adopt a retrofocusing design if the distance from the lens to the sensor is too great, which adds additional lens elements adding bulk and weight. Mirrorless cameras can avoid this because they allow the lens closer to the sensor.