Well to be nerdy we need something to be nerdy about. I'll have a bash but without sums or anything as its too early in the morning.
As anybody who has used large format cameras or enlargers knows diffraction at f64 isn't nearly the same level of problem as diffraction at even f22 on a 35mm camera. Diffraction is caused by light hitting the edges of the aperture blades. And as the lens is closed down this becomes more of a problem proportional to the size of the opening that the light is coming through as the angle of the light increases. So on a 35mm lens you have a tiny hole for the light to get through at f22, and the proportion of disturbed light is large. With a large format lens (say a 150 mm) even at f64 the hole made by the aperture blades is going to be something like the size of a 35mm lens at f5.6, so the proportion of disturbed light is small.
So f64 can be used without incurring the same level of unsharpness caused by diffraction in smaller formats.
Then I'll go nerdy now, because I think you've got your math wrong
😉 And I'll try to do it without mentioning sharpness too much so that people don't think I'm obsessed.
The problem with diffraction is that it turns rays of light into little discs; if these diffraction discs get too large, the image goes all fuzzy. I think on this we'll probably agree.
The size of the diffraction disc is actually independent of the focal length and only depends on the numerical aperture value; in other words, the diffraction disc at f/22 is always the same size, whether on an 12mm lens or on a 240mm lens, in spite of the apertures having wildly different diameters. If you look at the formula for the airy disc, you find that it's not only the physical diameter of the aperture that matters, but the focal length as well. Your observation that the aperture of a lens of short focal length at f/22 is much smaller geometrically than that of a long lens is correct, but then the focal length of the two lenses is different, too; in the formula for the airy disk, you have the focal length in the numerator and the diameter in the denominator, so the two cancel each other out and it's only the numerical aperture that counts.
This has a number of interesting consequences. For example, it means that on an APS-C sensor it doesn't make sense to stop down very far, because the airy discs quickly become larger than the pixel pitch of the sensor (beyond f/11 or so depending on the sensor) - I recently saw the calculation for f/22, where the airy disc is 15 µm in diameter, while on a 14MP APS-C camera the pixels are 5 µm wide. In the words of the poster there, it's like when someone gives you a 3mm felt-tip pen and tells you to fill in individual boxes on 1mm graph paper.
The primary reason why this matters less in large format is not that the lenses are physically larger or have longer focal lengths, but that the negative is larger. When making, say, a 30x40" print, the enlargement ratio from 35mm is about 30x, from 4x5" it's about 8x. So if you have a picture taken at f/64, the fuzzy discs gets enlarged either 30x where they turn the whole print into goo, or 8x where they are still manageable. In other words, a 4x5" negative simply has much more room and reserves for detail.
In enlarging it's somewhat similar - it's the ratio that counts. When enlarging 35mm negatives, it's very easy to reach enlargement factors of 10x or 20x. For 8x10" prints from 35mm film, the ratio is about 8x, from 4x5" negatives it's 2x (in other words if all you produce is 8x10" prints, you can basically print 4x5" negatives through the bottom of a bottle and they will look OK). When switching from large format to 35mm, it all suddenly becomes critical. In other words, you can print 4x5" negatives with your enlarger lens set to f/22, while if you do the same with 35mm negatives you get slightly mushy-looking prints - the diffraction discs are the same, only they get enlarged much more. So if you don't want the enlarged diffraction discs to turn your whole print fuzzy, it's a good idea not to stop down too far. This, in turn, means that you have little depth of field reserves, so you need a good enlarging lens, and a negative holder that holds your negatives flat, and you need to spend time to align your enlarger head and baseboard so that they are parallel.
However, there is a reason why it's worth putting all this effort into aligning your enlarger head that has nothing to do with sharpness, and this is the grainy look of film. Let's say you print from a film with moderately coarse grain (say, the grain is 10 µm in size) and you print it at f/22, where the size of the airy disc is 15 µm as above. In this case, diffraction kills the resolution of your film to the point that you can't discern individual grains any more,
no matter what the print size, because diffraction mushes them together into grays. So if you want to see grain in your prints, print at lower apertures.
This is consistent with my own darkroom experience. It's a real eye opener when you do this enlargement properly once in your darkroom and start printing at f/8 instead of f/16, only to find out that your 35mm prints look completely different and much crispier and better.
