Question

A compound microscope has an eyepiece of focal length $10cm$ and an objective of focal length $4cm.$ Calculate the magnification, if an object is kept at a distance of $5cm$ from the objective so that final image is formed at the least distance of distinct vision $\left(20cm\right):-$

Answer 1

Answer: 12

Given: Focal length of objective is $f_o=10cm$ and eyepiece $f_e=4cm$ , the object distance from objective is $u_o=-5cm$ and distance of distinct vision is $D=20cm$ .
From Lens formula distance of image from objective lens is,
$\frac{1}{v_o}=\frac{1}{f_o}+\frac{1}{u_o}$
$\frac{1}{v_o}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}$
$v_o=20cm$
The magnification of microscope is given by,
$m=\frac{|v_o|}{|u_o|}\left(1+\frac{D}{f_e}\right)$
$m=\frac{20}{5}\times \left(1+\frac{20}{10}\right)=12$ .