The DOF equations may look daunting and complicated but if you rearrange it slightly, then you could deduce whether a factor is directly or inversely proportional to DOF.

DOF(near) = s(H - f)/(H + s - 2f)

Rearrange the denominator, becomes s(H - f)/[H - s + (2s - 2f)]

DOF(near) = s(H - f)/[H - s + 2(s - f)]

DOF(far) = s(H - f)/(H - s)

DOF = DOF(far) - DOF (near)

So if s=f, then DOF = zero because DOF(far)=DOF(near) although it's not practical.

The closer s is to f, the smaller is s-f, meaning that DOF(far) will be nearer to DOF(near) ==> shallower DOF. Therefore for a given focal length, the closer you are to the subject (i.e. smaller s makes s-f smaller), the shallower the DOF is. For a given subject distance, the longer the focal length you use (i.e. bigger f makes s-f smaller), the shallower the DOF.

Other relationships between DOF and aperture, focal length etc. can be deduced in similar fashion.

http://www.dofmaster.com/equations.html
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