Question

An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?

Answer 1

Let the image is formed at normal near point 25 cm.

∴ Angular magnification = (1 + d/fe) = (1 + 25/5) = 6.

Magnification of the objective lens, m = 30/6 = 5

As, m = v₀/-u₀ ⇒ v₀/-u₀

∴ v₀ = - 5u₀

As, 1/v₀ - 1/u₀ = 1/f₀

∴ 1/5u₀ - 1/u₀ = 1/1.25, (-1 - 5)/5u₀ = 1/1.25, -6/5u₀ = 1/1.25

∴ u₀ = (-6 x 1.25)/5 = - 1.5cm

∴ v₀ = - 5u₀ = - 5 x (-1.5) = 7.5cm

As, 1/u_e = 1/v_e - 1/f_e 

∴ 1/u_e = 1/-25 - 1/5 = (-1 - 5)/25 = -6/25

∴ u_e = - 4.17cm

The separation between the objective and the eyepiece 

= 7.5 + 4.17 = 11.67 cm