Question

An object viewed from a near point distance of $25\, cm$, using a microscopic lens with magnification ' $6$ ', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length $0.6 \,m$, if the focal length of the eyepiece is equal to ______$cm$.

Answer 1

For simple microscope,
$m=1+\frac{D}{f_{0}} $
$6=1+\frac{D}{f_{0}}$
$5=\frac{25}{f_{0}} $
$f_{0}=5 \,cm$
For compound microscope,
$m=\frac{l \cdot D}{f_{0} \cdot f_{e}} $
$12=\frac{60 \times 25}{5 \cdot f_{e}} $
$f_{e}=25 \,cm$