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A 50mm prime lens, whether APS-C or Full-frame is designed around the 35mm format. As such, is the angle of view actually different on a DX/APS-C crop sensor or are we just seeing less of the full frame angle of view?

I think that the angle of view, depth of field, and compression are the same as on an FX/Full frame but we are seeing only middle, correct?

If so, then isn't it the case that a 50 1.4 is giving the same DOF on full-frame as DX but because we are seeing less, we have to stand further away, thus the "increase in DOF" on a DX?

More importantly, and the thrust of my question, is that the perspective/compression is the same regardless of crop factor on 35mm format lenses, right?

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I think this is pretty well covered under What is "angle of view" in photography? – mattdm Nov 19 '12 at 15:03
up vote 7 down vote accepted

In short, yes, it is actually different, but only because the angle of view is by definition measured to the edge of your view — which is the edge of the sensor, which is (again by definition) different on APS-C.

Your statement

I think that the angle of view, depth of field, and compression are the same as on an FX/Full frame but we are seeing only middle, correct?

is completely correct (with that caveat). But, "is the angle of view actually different on a DX/APS-C crop sensor or are we just seeing less of the full frame angle of view" is meaningless, because it's called angle of view because the view is what's measured. One could measure the angle to the edge of the projected circle of light from the back of the lens, but that's not particularly useful since it's not recorded. The exercise in my answer to What is "angle of view" in photography? should make this all clear.

And you're right about the depth of field, too. More on that at Why does a bigger sensor lead to a shallower depth of field? and Can a smaller sensor's "crop factor" be used to calculate the exact increase in depth of field?.

And, you're also right about the effect on perspective: that's solely a matter of where you stand. That's covered at What is background compression?, and to quote ex-ms from an answer there:

If you take a shot with a wide-angle lens and crop down to the very centre, you would have the same background compression as if you took the shot with a telephoto lens.

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So to summarize: The angle of view, depth of dield, and compression are the same for all 50mm lenses, whether the lens was designed for full frame or crop sensor. But because you're only seeing the center portion of the image with a crop sensor, you have to farther from the subject to get the same field of view. That farther distance changes the depth of field and compression. But the angle of view of the lens is not affected by where you stand. – Stainsor Nov 19 '12 at 22:47
Got it. The "Full Frame Equivalent" conversion never sat right with me. But I see what you're saying about "Angle of View", makes sense. thanks – camflan Nov 19 '12 at 23:03

You are correct in that the compression/perspective distortions are the same, and that it is the same image on full frame cropped, but angle of view (FOV) is different. This is because FOV is given by fov=2*atan(sensorsize/(2*f^2)).

This is why I find the "focal length conversion" rule of thumb misleading, as people has to realize it is only regarding the resulting FOV it works. All the other things that depend on the focal length are unchanged. Converting the "focal length" to 35mm eq. only makes sense to a person who has an intuitive relationship to the FOV on fullframe, who can tell how wide an area is covered at a given distance and focal length, and then divide the area by 1.6. But for digital age newcomers who never used a 35mm to a level, where such intuition arise, it is pointless.

A 50mm equivalent lens (30mm, practically 28-35mm) on a crop sensor will still distort the face too much for portraits as it would on the full frame. Less, due to standing farther from the target to get the same framing.

Another thing to note is that you are wasting a lot of the light that goes through the lens, than if the lens was designed to place it on the 24mm wide sensor.

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We are just seeing less of the view. Its cropped. We call them crop sensor cameras.

I too find the whole "lens equivalent" discussion a bad thing. It doesn't describe what is actually happening, and its only approximately right in what it does cover.

Consider your 50mm F1.4 lens. Mount it on an APS-C body. Then mount it on a full frame body. In both cases, its a 50mm F1.4 lens. You could also mount it on a view camera, which typically have very large sensors. Again, it would still be a 50mm F1.4 lens. On the medium format sensor, the image will cover a larger viewing angle. Yet again, the lens doesn't know its mounted on a view camera.

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When both APS-C and a full frame have a lens that caters for both having the same angle of view it results in both having different perspective even though having the same angle in horizontal sense. It means that if the full frame has a 50mm, which is the focal length for viewing perspective as the human eye does, the APS-C will need smaller focal length to achieve the same viewing angle. However perspective will NOT be as the human eye sees, objects will appear oblong when near and object will more quickly become smaller with the distance from the camera. This is one of the reasons video-dedicated cameras (not DSLRs) have that typical perspective besides having a higher depth of field.

3 main factors typify the image: viewing angle, perspective and depth of field.

Observe images of 6 x 6 cm camera's or even larger to understand that concept of perspective.

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This is not correct. The only factor in perspective is position; perspective distortion is not a lens property. It's true that you'll need a shorter focal length on a smaller sensor to get the same angle of view, but if you have that, and stand in the same place so the framing is the same, the perspective will necessarily be the same too. – mattdm Mar 8 '15 at 22:09
When both APS-C and a full frame have a lens that caters for both having the same angle of view How does that happen?? – BBking Mar 9 '15 at 1:50
@BBking I understand it to mean two lenses, one 75mm meant for full frame and one 50mm meant for (1.5×) APS-C. – mattdm Mar 9 '15 at 3:52
OK, and it makes more sense that way. But the way it was written makes it sound like there is only 1 lens to suit both formats. EDIT: Incase anyone was interested, I didn't downvote. – BBking Mar 9 '15 at 10:39
@BBking I downvoted. As noted, this answer is incorrect; if you stand in the same place (and the subject does too), perspective will always be the same, regardless of sensor size or focal length. It's a fairly common misunderstanding, but let's not perpetuate it. – mattdm Mar 9 '15 at 14:52

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