[foldr]

If you double the focal length you also have to double the sensor dimensions (to get the same angle of view) and hence double the size of the CoC - so you end up with f^2/f = f. That is, you double the numerator in the DoF formula because the CoC has doubled, and quadruple the denominator because the focal length has doubled, with the end result that the DoF halves.

Your mistake is one that’s easy to make and one that I’ve made myself before. We’re not trolling you. You’re just losing track of a factor of f and thereby getting the wrong result.

By the way, I also agree with your overall point about smaller sensor cameras being better suited to macro photography. It’s just that your f512 claim is based on a mistaken calculation.

[defaultname]

"Your mistake"

There is no mistake. Your first paragraph is unfortunately founded on some misunderstandings of optics, however I calculated the hyperfocal length for an equivalent ASP-C 35mm system and an iPhone at the same crop (which anyone with an SLR and an iPhone can replicate in moments). The iPhone has a dramatically higher DoF. There are no mistakes in that calculation. This is the reason why you need computational bokeh. It's why it's so easy for everything to always be in focus. Could someone contrive ridiculous focal length / f-ratio / CoC parameters? Of course they can -- it's just a function with parameters that you punch in, and they can offset. In actual reality, however, short focal length is the primary input into why small cameras feature larger depths of field. Why we talk about the equivalent aperture in the way that we talk about equivalent focal length.

sudosysgen's argument in the end seems to distill down to "yes, but compare it via the equivalent DoF f-stop on the larger camera" which is a short circuit of the entire argument. It is basically saying that AMC is worth the same as Apple if AMC shares were each worth $4636.

Okay.

[sudosysgen]

That's not how it works. If I take a picture with 2x crop sensor at 100mm f/2 it is going to be exactly the same picture as at 50mm f/4 on a FF camera. Its just how it works. They have proven it using the DOF equation by showing that scaling the CoC factor down with the focal length and scaling the focal length down means you have the same DoF as long as the actual aperture diameter is the same, algebraically. I gave you an explanation of why it is the same because the solid angle is preserved. In the end you're making the typical photographer mistake of misunderstanding crop factor.