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. Find the focal length of the eyepiece.

Answer 1

For the compound microscope, we have:
Magnifying power, m = 100

Focal length of the objective, f₀ = 0.5 cm  Tube length,   l = 6.5 cm

Since the image is formed at infinity, the real image produced by the objective lens should lie on the focus of the eyepiece.

∴ v_o + f_e = 6.5 cm  .....(1)

The magnifying power for normal adjustment is given by

m = `v_0/u_0 × D/f_e`

=`-[1-v_0/f_0]D/f_e`

`=> 100 = -[1-v_0/0.5] × 25/f_e`

⇒ 2v_o -4f_e = 1 ..(2)

On solving equations (1) and (2), we get:

v₀ =4.5 cm and f_e =2 cm

Thus, the focal length of the eyepiece is 2 cm.