\(M =\frac{ f _{0}}{ f _{ e }}\)
The magnification of the eyepiece lens is given by:
\(M _{ e }=\frac{ f _{e}}{ f _{e}+ u }=\frac{ L _{ I }}{ L _{ O }}\)
Here, \(L _{1}\) is the length of the image and \(L _{0}\) is the length of the object.
Now for the eypiece lens, the distance of the object is \(-\left(f_{0}+f_{e}\right)\)
\(\frac{f_{e}}{f_{e}-\left(f_{0}+f_{e}\right)}=\frac{-I}{L}\)
\(\Rightarrow \frac{ f _{ e }}{ f _{0}}=\frac{I}{ L }\)
i.e \(M =\frac{ f _{0}}{ f _{ e }}=\frac{ L }{ I }\)