Question

A compound microscope consists of two convex lenses of focal length $2$cm and $5$cm. When an object is kept at a distance of $2.1$cm from the objective, a virtual and magnified image is formed $25$cm from the eye piece. Calculate the magnifying power of the microscope.

Answer 1

focal length of eye-piece $f_e=5cm$

focal length of objective lens $f_o=2cm$

$u_o=-2.1cm$ (using sign conventions)

$D=25cm$

$v_e=25cm$

by the lens formula

$\Rightarrow \frac{1}{v_o}-\frac{1}{u_o}=\frac{1}{f_0}$

$\Rightarrow \frac{1}{v_o}=\frac{1}{2}+\frac{1}{2.1}\Rightarrow v_o=1.024cm$

magnification of microscope

$\Rightarrow m=\frac{u_o}{v_o}(1+\frac{D}{f_e})\Rightarrow m=\frac{2.1}{1.024}(1+\frac{25}{5})\Rightarrow m=12.3$