# How does using a lens with some focal length on a full frame camera differ from using a lens with “equivalent” focal lens on a crop camera?

As an example, a 35mm lens on a crop body (such as Nikon DX) is said to be "equivalent" to a 50mm lens on a full frame body. Equivalent here means that they will have the same field of view, but what other aspects will change or stay the same between the two? I'm thinking about things like perspective, bokeh, and depth of field (assuming the same aperture being used on both lenses).

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It will be cool if someone can post two images of the same scene - one from 35mm on DX and the other one from FF with 50mm. Both with the same aperture, preferably smaller one. The scene should be eg. table with some stuff on it - just to compare the DOF, where they will differ the most. – Petr Újezdský Apr 20 '12 at 17:57
I think my answer (and the other answers as well) to Does my crop sensor camera actually turn my lenses into a longer focal length? covers this pretty well. – mattdm Apr 20 '12 at 17:59
I've had this question myself - my main area of interest was the perspective change – DHall Apr 20 '12 at 19:57
You're making this more complicated than need be. Perspective is literally a matter of where you stand. Only moving can change it. Therefore, if two camera/lens combinations give the same field of view, and you put them in the same place, perspective will be identical. – mattdm Apr 20 '12 at 21:35
@pida you mean like this: mattgrum.com/FF_vs_APS-C.jpg – Matt Grum Apr 20 '12 at 23:44

It is well known that in order to get the equivalent focal length, you have to multiply the real focal length by the crop factor. Thus, a 35 mm lens on a DX body is equivalent to a 53 mm on FX (the DX crop factor is 1.52).

What is less known is that the same crop factor applies to the F-number. Thus, a 35 mm f/1.8 on DX is equivalent to a 53 mm f/2.7 on FX. By “equivalent” F-number I mean that in both situations you will get:

• the same light gathering power, i.e. the same number of photons collected from a given scene with a given exposure time,
• the same depth of field (c.f. this answer by mattdm)
• the same ability to blur the background, which is related to but not the same as depth of field.

Now, if you use the same exposure time, the two situations will obviously not give the same ISO. If you have ISO 200 at f/1.8 on the DX body, you would need ISO 460 at f/2.7 on FX. But you should nevertheless expect the same amount of noise, assuming both sensors have the same intrinsic quality.

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I'm a little bit confused - you say "same light gathering power" and yet, you say that the ISO should be different. Or, are you implying that due to smaller sensor, the same number of photons will generate a brighter image? Also, @mattgram claims for same exposure for same f-number. Can you please elaborate? – ysap May 30 '12 at 10:28
@ysap, be aware that the answer here assumes that the f-number is NOT the same - he has stopped down the full-frame setup in order to get the same depth of field as the crop-sensor setup. Hence, ISO or shutter speed must be adjusted to give the same exposure. It is normal in these comparisons to let the aperture stay constant and simply state that DOF is shallower for the full-frame setup. It's just a matter of choosing a different variable in the setup :) – Staale S May 30 '12 at 12:55
Multiplying the f/number by the crop factor gives you the same number of photons per image, (i.e. the same light gathering power, using the same f/stop gives the same number of photons per unit area of the sensor. You cannot say in general whether or not either scheme yields the same exposure at a given ISO as it depends on the saturation point of the pixels, however if the saturation point is the same, if you multiply the f-stop by the crop factor you'll also have to multiply the ISO by the crop factor to achieve the same "brightness". – Matt Grum May 30 '12 at 13:23
@Matt Grum: You have to multiply the ISO by the crop factor squared. – Edgar Bonet May 31 '12 at 9:14
@Edgar, you're right it's the ratio of areas so crop factor squared, can't edit the comment now though... – Matt Grum May 31 '12 at 9:29

Assuming the same scene and focal lengths chosen to match field of view:

• Perspective will be the same, as it is a function of subject distance.

• Exposure will be the same for he same f-stop.

• Depth of field will be different for the same f-stop, as it is a function of absolute aperture size, 50/2.8 is a bigger quantity than 35/2.8, so the 50mm lens will have shallower depth of field.

• Bokeh in the strictest sense is dependant on the lens design and construction so there is no overall trend.

• The larger format will in general resolve more detail.

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Calling it "equivalent" is just shorthand, and often not very accurate.

First, the lens doesn't know what body its mounted on. You can mount the same 35mm lens on a crop frame APS-C, a full frame, and on a view camera.

Calling the camera a crop-frame is the important one, it takes the same photo, but crops it. When you crop an image, you change it. If you shoot at the same camera/lens to subject length with crop and FF bodies, the perspective will be identical -- it will be easier to see when you crop the FF image.

Most definitely, the depth of field will not be the same. You get smaller depth-of-field when the sensor/film is bigger relative to the focal length of the lens.

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