Is the angle of view actually different on APS-C?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.