I don't know what to say to that. . I mean, if you have been on these forums for almost 10 years, and still don't understand the impact that sensor size has on DOF, then, well ...... that's unfortunate.
Maybe this will make sense:
Shooting on a full frame sensor, and then cropping the image, is the same as shooting on a smaller sensor (all else being equal). . And we all know that the same shot with the same framing on a crop sensor has greater DOF than on a full frame sensor. . So the same thing applies to cropping in to a large image - in fact, that's why the term "crop sensor" was coined.
But this really isn't supposed to be discussion about sensor sizes - it's supposed to be about a 1.7x tele-extender. . Sorry for the detour.
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There is no contradiction here. You can think of DOF in at least those two ways: the DOF of the field of view of the entire image, and the DOF of a normalized subject. Since you, personally, always target the entire frame, then thinking in terms of the frame works out fine. People who are focal-length-limited, however, have a more direct handle on subject DOF when they consider aperture size, subject distance, and subject size.

