General rule of resolution of optical systems

[Marketo]

According to Faynman Lectures on physics in the chapter of geometrical vol1 ch27, the general rule for the resolution on any optical instrument is this: Two different point sources can be resolved only if one source is focused at such a point that the times for the maximal rays from the other source to reach that point, as compared with its own true image point, differ by more than one period.

and Faynman resume this in the next expression t2-t1 > period

Faynman also says that if D is the distancee between the two soure points and if θ is the angle of the lens opening, the last equation is equivalent to say that d must exceed λ/(n sinθ)

Faynman also says that the angle θ is about λ/D, where D is the lens diameter.

I can't find an explanation of all of this, and it would be write to understand it because I have to talk about telescope. The chapter of Faynman lectures where you can find all of this is attached for this thread

 

[JeffKoch]

There really is no single hard-limit formula for the resolution of an optical system, because you have to define what exactly you mean by "resolve". Intensity dip between the images is 50%? 20%? Equal to the RMS noise level? What is the spatial period of the noise? Etc. To characterize an optical system, you can use a modulation transfer function, or a point-spread function, but both characterizations are curves, not single numbers.