Circle of confusion and the thin lens equation

I have spent a little time working out some rules of thumb regarding depth of field, thin lens equation, lens distortion and compression and a few other obvious things. I find that looking at the math helps with understanding these concepts in depth. The full article can be found here. and I summarize it as follows:

  • Higher resolution sensors can be considered to have a smaller depth of field as images can be enlarged more.
  • Depth of field depends only on the aperture but no the focal length, as long as image size on the sensor is kept constant.
  • Depth of field behind the plane of focus is bigger for short focal length lenses, and smaller for long focal length lenses. Thus, telephoto lenses will defocus distant objects faster.
  • Any two lenses with the same maximum aperture will have identical depth of field. However, long focal length lenses will have a smoother bokeh, and appear to have a shallower focal length due to a narrower angle of view, and the fact that they defocus distant objects faster.
  • Perspective distortion occurs because the derivative of image size w.r.t. object distance is inversely proportional to the square of distance. As short focal length lenses are used at short distances, they exhibit distortion. In contrast, long focal length lenses exhibit compression.
  • Given a lens with focal length f1 and maximum f-stop number n1, used on a camera with a sensor having diagonal length of d1, if we want to take exactly the same picture with another camera with a sensor of diagonal d2, we must use a lens with focal length f2=f1*d2/d1, at aperture n2=n1*d2/d1
  • The film medium format look is hard to replicate with digital cameras because medium format film is physically bigger . Therefore, medium format film cameras have a shallower depth of field than digital cameras. For example, to replicate the Pentax 6x7 105mm f2.4 lens one would need to use an f1.1 lens in the full frame format. This lens is impossible to replicate using cropped sensor and micro four thirds cameras. It is also difficult to replicate it using digital medium format, as lenses with equivalent f-stops are not readily available.