This is theoretically correct, but practically wrong. Only one point (or plane) is ever in focus; everything in front of it or behind it is technically OOF, however slight the difference. But, human vision and camera sensors can only resolve so much detail, which makes the zone in front of and behind the plane of focus seem focused too - simply because the OOF blur is so small that it seems sharp. Technically, "apparent DOF" would be a better term than "DOF". If you blow up the image - be it by cropping the image, or by using a longer equivalent focal length - the same amount of blur is going to be enlarged more. That means the area where the OOF blur is smaller than we can see (aka smaller than the circle of confusion) decreases, giving a shallower apparent DOF.My head hurts reading the replies, but here's what I know from experience, and I'm avoiding the DOF Calc.
If you use the same exact lens, and you shoot the subject at the same exact distance, DOF should be the same, but the APS-C will give a tighter crop. It's the same as if you shot it with the FF camera, and then just cropped in LR. DOF does not change just because you cropped the picture.
I think you're mixing up lenses and bodies here; the FF camera needs the 75mm lens to give the equivalent field of view to the APSC with 50mm. But yes, the longer absolute focal length coupled with the same f-number means a larger physical aperture opening, and since subject distance and equivalent focal lengths are the same, the FF body/lens combo will have shallower DOF.If you move positions (i.e. getting closer with the FF or moving further away with the crop) to get similar framing, then the DOF should be less on the FF, because you are now closer to the subject. The focal length and the physical aperture size has not changed. If, however, you grabbed a 75mm lens to shoot with the FF and a 50mm lens on the crop (assuming a 1.5 crop), and you kept distance to subject the same, then DOF will be driven by the physical aperture size, so if f/stops were the same (e.g. both 1.4), then the FF should have shallower DOF because 50/1.4=35.7mm vs. 75/1.4=53mm.
yup, the look is more important than being right or wrongThat's the way I understand it, but actually don't really care, lol. I have the lenses I have (50/1.4 and 85/1.8 on FF and 22/2 on my EOS-M) and I like the look of these lenses a lot, so if I'm wrong, I'm wrong
Also, if "viewing distance" to the picture comes into play here, well then I'll just keep quiet. My viewing distance is just about always 2 feet (distnance from my chair to my monitor)
viewing distance... well that's a whole different matter, more related to output size (monitor or print size). So long as you're close enough to the image to see the maximum detail resolved by the monitor or print, it doesn't have any influence on DOF. If you get further, apparent DOF will become deeper, but that's true regardless of which camera/lens combo you used.
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for what it's worth flash, I also limited myself to the simple formula that Focal length / Physical aperture size = f-number, throughout this discussion. Bokeh... indeed let's not go there