Question

A compound microscope consists of two convex lenses having focal length of 1.5 cm and 5 cm. When an object is kept at a distance of 1.6 cm from the objective, the final image is virtual and lies at a distance of 25 cm from the eyepiece. Calculate magnifying power of the compound microscope in this set-up.

Answer 1

Given: D = 25 cm

u_o = −1.6 cm

f_o = 1.5 cm

f_e = 5 cm

M = ?

For the objective,

`-1/u_o + 1/v_o = 1/f_0`

⇒ `1/v_o = 1/f_o + 1/u_0`

= `1/1.5 + (1/-1.6)`

= `10[1/15 - 1/16]`

`1/v_o = 10/(15 xx 16)`

⇒ v_o = `(16 xx 15)/10`

= 1.6 × 15 cm

= 24 cm

Now magnifying power,

|m| = `v_o/(|u_o|) (1 + D/f_e)`

= `(1.6 xx 15)/1.6 [1 + 25/5]`

= `24/1.6 [30/5]`

= `24/1.6 xx 6`

= 15 × 6

= 90