If we need a magnification of \(375\) from a compound microscope of tube length \(150\; \mathrm{mm}\) and an objective of focal length \(5\; \mathrm{mm}\), the focal length of the eye-piece, should be close to.....\(mm\)

focal length of objective lens is small \(u_{0} \simeq f _{0}\). Alos as focal length of eye is small

\(v _{0} \simeq L\)

\( M =\frac{ L }{+ f _{0}}\left(1+\frac{ d }{ f _{ e }}\right) \)

\(\Rightarrow 375=\frac{150}{5}\left(1+\frac{250}{ f _{ e }}\right)\)

\(\Rightarrow \frac{375}{30}=\left(1+\frac{250}{f_{e}}\right)\)

\(\Rightarrow \frac{375}{30}-1=\frac{250}{f_{e}}\)

\(\Rightarrow \frac{345}{30}=\frac{250}{f_{e}}\)

\(\Rightarrow f _{e}=2.2 \;cm\)

\(F _{ e }=22\; mm\)