I was curious if I could cheat my way around having to focus stack an object by using different lenses. Playing with the Depth of Field calculator I noticed something interesting: No matter what focal length I select the depth of field for the same angle of view (at the subject) is constant.
For example, fixing sensor format at APS-C, aparture at f/22, and a supposing I need a distance from subject of 2m for a 300mm lens I get a depth of field of 3cm. I get the same DoF with a 600mm lens at 4m, 150mm at 1m, and 75mm at 0.5m.
Is this a quirk of practical lenses (or of that calculator), or is there a theoretical constraint here, and if the latter can someone show the math and theory?
Update: To clarify some potential confusion in the first paragraph, the question may be restated as follows: Given a fixed sensor, object, aperture, and magnification, is it possible to vary Depth of Field by varying lens focal length?