Question

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

Answer 1

focal length of objective lens, $f_o$ = 0.5cm

and tube length = 6.5cm

we know, from compound microscope,

tube length = $v_0+f_e$ = 6.5cm.........(1)

magnifying power , m = $-\left[1-\frac{v_0}{f_0}\right]\frac{D}{f_e}$

Take , D = 25cm, $f_0=0.5cm$

100 = $-\left[1-\frac{v_0}{0.5}\right]\frac{25}{f_e}$

$100f_e=-(1-2v_0)25$

$4f_e=-1+2v_0$

$2v_0-4f_e=1$..........(2)

from equations (1) and (2),

$v_0=4.5cm,f_e=2cm$

hence, focal length of the eyepiece is 2cm.