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 $\left(20 cm\right):-$

Answer 1

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,
$m=\frac{\left|v_{o}\right|}{\left|u_{o}\right|}\left(1 + \frac{D}{f_{e}}\right)$
$m=\frac{20}{5}\times \left(1 + \frac{20}{10}\right)=12$ .