You are wrong. Changing the print size WILL expand or contract the apparent depth of field in the print. Magnification is, in fact, part of how depth-of-field is defined. It's physics and geometry. You cannot simply wish the magnification term out of the thin-lens depth-of-field equation.If you have a photograph with narrow depth of field such that foreground and distant objects are out of focus and the middle area is in focus, changing the print size will not expand or contract the apparent depth of field in the print.
Honestly, I'm surprised this is not obvious. Who among us has not printed an apparently-sharp 35mm contact print, only to find out that it looks OOF at 8x10? Why do we use loupes on our ground glass? According to your statement, if it looks sharp at 4x5 it should be sharp at any size.
Absolutely! Depth of field has no meaning outside the context of VIEWING. That is why it is defined, from the beginning, using magnification, which is obviously important when it comes to perception of details (else we would have never invented the microscope). When it comes to viewing reflective media, the circle of confusion has to be CHOSEN based on visual perception. It could be .5mm or it could be 4 inches. Once you have chosen a circle of confusion for the print, THEN you can meaningfully talk about depth of field when taking photographs. Circles of confusion at any intermediate stage (such as on the camera film) is basically irrelevant. You could shoot to a small format and enlarge 10x or shoot to a format twice as big and enlarge 5x. The 'film CoC' will be different in each case but the depth of field will be the same."A different maximum circle of confusion also applies for each print size and viewing distance combination": Cambridge in colour.
At at agreed-upon print CoC, all photographs taken at the same aperture (as distinct from f-stop) and enlarged to the same magnification will have the same depth of field characteristics, completely regardless of lens focal length, film format, or whether you are using 8mm or 20x24 film.
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