An object viewed from a near point distance of
$25 \mathrm{~cm}$, 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 $0.6 \mathrm{~m}$, if the focal length of the eyepiece is equal to__________ $\mathrm{cm}$.
For simple microscope,
$\mathrm{m}=1+\frac{\mathrm{D}}{\mathrm{f}_{0}}$
$6=1+\frac{\mathrm{D}}{\mathrm{f}_{0}}$
$5=\frac{25}{\mathrm{f}_{0}}$
$\mathrm{f}_{0}=5 \mathrm{~cm}$
For compound microscope,
$m=\frac{\ell \cdot D}{f_{0} \cdot f_{e}}$
$12=\frac{60 \times 25}{5 \cdot f_{e}}$
$\mathrm{f}_{\mathrm{c}}=25 \mathrm{~cm}$
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