Question

A compound microscope has a magnifying power of $100$ when the image is formed at infinity. The objective has a focal length of $0.5$ cm and the tube length is $6.5$ cm. Then the focal length of the eyepiece is

• A. $2cm$
• B. $2.5cm$
• C. $3.25cm$
• D. $4cm$

Answer 1

The correct option is C $3.25cm$

The magnifying power of a compound microscope is given by:
$m=\frac{LD}{f_o{f}_e}$

$\Rightarrow f_e=\frac{LD}{f_{o}m}=\frac{6.5\times 2.5}{0.5\times 100}$

Substituting the respective values, we get $f_e=3.25$