Question

A compound microscope has an eye piece of focal length $10cm$ and an objective of focal length $4cm$. If an object is kept at a distance of $5cm$ from the objective, so that the final image is formed at the least distance of distinct vision $20cm$, calculate the magnification.

• A. $12$
• B. $11$
• C. $10$
• D. $13$

Answer 1

The correct option is A $12$

Given
$u_0=-5cm,f_0=4cm,f_e=10cm,D=20cm.$

Applying lens formula at objective lens
$\frac{1}{f_0}=\frac{1}{v_0}-\frac{1}{u_0}$
$\frac{1}{v_0}=\frac{1}{4}+\frac{1}{-5}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}{v}_0=20cm$
Magnification of compound microscope at least distance of distinct vision is given by
$M=\frac{v_0}{|u_0|}(1+\frac{D}{f_e})=\frac{20}{5}(1+\frac{20}{10})=12$