Assumption: You have 2 lenses, one for 35mm sensor camera and another is specially made for APS-C; both are 50mm in focal length and f/2 maximum apeture.
Question #1: Do the both lenses produce identical result?
Answer: Every lens has its own subjective characterstics, so they are going to be different. For now let us ignore that subjective characteristics and lets see what are the real objective differences. Remember one is made to cover 35mm sensor and another is specialized for APS-C sensor. F numbers and focal lengths are identical for these two lenses. The very obvious difference between these two is image circle. Imgae circle must cover the sensor in order to fill sensor with image; if image circle doesn’t cover the sensor then corners of the sensor will be balck/vignetted. Refer to the picture below. Same focal length lenses with different sensor sizes will produce different sized images while the subject is at the same distance. This simply means - lens for the bigger sensor, due to it’s bigger image circle will cover more areas in the virtical plane (vertical to the lens axis) of the subject. If the lens with bigger image circle is used with smaller sensor – the lens will produce same image circle but the sensor only can use smaller portion of it. This is the reason it makes sense to produce dedicated lens for the smaller sensor as lens construction can be far cheaper when image cicle is smaller. In a nutshell dedicated lenses produced for smaller sensors can not be used with bigger sensor even if the lens mounts are compatible. But opposite is true – a lens made for bigger sensor can be used on cropped sensors. Effective image circle for any sensor remains same. Effective image circle is the smallest circle that can cover the entire sensor. Hope this is clear! like muddy water? :)
Question #2: I heard 50mm on full-frame becomes 50*1.5 = 75mm or 50*1.6 = 80mm on APS-C sensors? 1.5 and 1.6 are two common crop factors for APS-C cameras.
Answer: No, not at all. 50mm focal length is 50mm always no matter how big and small the sensor is. People make wrong statements because – due to the smaller sensor size on APS-C cameras the minimum distance to fully cover a subject is more for APS-C cameras compare to the full-frames. Look at the picture above – smaller sensor covers smaller portion of the subject compare to the bigger sensor. In order to cover equal area of the subject, distance of the subject for APS-C has to be more. In this case a full-frame compatible lens and APS-C dedicated lens will produce same result on APS-C sensor. The APS-C special lens just has smaller image circle, as bigger image circle is not required for smaller sensor. So it is true that field of view of 50mm lens on APS-C sensor is like the field of view of 75/80mm lens on full-frame again just due to smaller effective image circle. Optical behavior of a 50mm lens is same on any sensor irrespective of its size. The general belief APS-C transforms a normal (say 50mm) lens into a telephoto lens; that’s not true. APS-C just crops the frame when subject is at the same distance. If you crop a full-frame image yourself with the 1.5/1.6, you will get the same result. Crop, crop and crop – nothing else is different on APS-C.
Question #3: I heard DoF is deeper on APS-C sensors – is that true?
Answer: It’s not true but there is something into it. Again it’s all about image circle and/or sensor size. If you use 50 lens(es) on both full-frame and APS-C cameras, with a subject with same distance from the camera and if the aperture is identical on both the cameras then DoF is going to be identical on both the cameras. But remember due to the smaller effective image circle on APS-C cameras, in order to capture same sized subject the camera needs to move further from the subject. With the same aperture and same focal length DoF increases with distance. You got it.
Question #4: According what you said – it looks like there is no reason for lens makers to make special lenses for cropped sensors and full-frame lenses will work well.
Answer: Lens construction becomes cheaper when the image circle is smaller. Though with the same focal length and same aperture the lens girth would be same for any sensor; but bigger the sensor performance at the edge becomes more critical. It adds a lot of cost to make performance at the edge better. Cropped lenses need lower edge performance simply because much of its edges are cropped; but of course remaining “edges” are expected to be acceptable. Aspherical design makes the edge performance better and we know aspherical lenses cost a fortune.
Question #5: Ok, which one should I buy - the smaller sensor or full-frame or even bigger like medium format?
Answer: Small sensors have some advantages – total gears will be small in size and weight, cost is less due to smaller sensor size and smaller image circle of the lens. Since smaller sensors generally produce smaller image files – continuous shooting and FPS performance can be achieved more on smaller sensor cameras with similar technology. The cameras with bigger sensors have advantages too – more usable image area, close distance to cover same size subject. Also remember, smaller sensor cameras requires wider focal length lenses in order to cover same subject area at the same distance. As we know wider lenses make images uncompressed which may not look good in most of the times. So bigger sensors are better for photographing landscape, building etc. everything else depends on person and somewhat on the application.
To capture wide perspective you need wider focal length on smaller sensor. To capture same wide perspective of 28mm lens on full-frame camera, you need 18mm lens on APS-C, and 14mm on micro43. Even though coverage can be equaled in this way but image compression gets completely changed when focal length changes.
For telephoto, popular belief is smaller sensor is better as you can go further from the subject to shoot it. The reality is not you can go further but you are forced to go further otherwise the image will not fit in the sensor. With same focal length lens and same distance with the subject – the images on APS-C and full-frame will be different in size with same compression characteristics. That simply means, if you crop the full-frame image it can give you the size of APS-C. Keeping the compression ratio same if you can go closer to the subject you can get better details – so image quality wise bigger frame is always better. Bigger is better – for image quality. But that does not mean bigger sensor is better for every practical thing. Bigger sensors are normally slower due to the large file size it produces. Bigger sensor translates to bigger camera housing – which is pain in that three-letter word my dad asked not to use. Bigger cameras cost more; bigger cameras are not easy to handhold in many situations. Finally bigger and smaller sensor would not show noticeable differences in image quality if not used in very large screen or large printing. So after knowing all the facts, practically you can buy an APS-C or Micro43 without practically loosing anything while saving some big bucks, gaining better movability and also can buy more dedicated lenses as they cost less compare to the lenses made for bigger sensors.