Astronomical telescope: derivation - greatest magnification (detail) formula

[jemerlia]

Homework Statement

I am seeking a derivation of the formula for greatest detail or maximum resolution of an astronomical telescope, which is:

Homework Equations

M = fo/foe where:

M: magnification
fo: focal length of objective lens
foe: distance of primary image from the eyepiece

N.B. Of course, the final image (seen through the eyepiece) is at the eye's near point

The Attempt at a Solution

Clearly the ratio di/do is important but I am uncertain about how to proceed from here. The formula is puzzling because it seems disjoint (related to two different lenses). Any help gratefully received. Sadly, geometric proofs are not my strongpoint! :)

Many thanks

 

[voko]

It is unclear what you want to obtain. Maximum magnification or maximum resolution? These are quite different.