# A microscope consists of two convex 20 cm apart. Where must the object be placed so that the final virtual image is at a distance of 25 cm from the eye ?

Q: A microscope consists of two convex 20 cm apart. Where must the object be placed so that the final virtual image is at a distance of 25 cm from the eye ?
(f_o = 2 cm , f_e = 5 cm)

Sol: For the eyepiece, focal length

f = fe = +5 cm; v = ve =-25 cm , u = ue = ? substituting in

$\large \frac{1}{f} = \frac{1}{v} – \frac{1}{u}$

$\large \frac{1}{5} = \frac{1}{-25} – \frac{1}{u_e}$

ue = -25/6 cm

object for the eyepiece is to be at a distance of 25/6 cm to its left.

But vo + ue =20 cm where ue = 25/6 cm

vo = 20 – ue = 20-25/6 = 95/6 cm

For the objective, v=vo = +95/6 cm

f = fo =+2 cm; u = ?

$\large \frac{1}{f} = \frac{1}{v} – \frac{1}{u}$

$\large \frac{1}{2} = \frac{6}{95} – \frac{1}{u}$

u = -190/83 = -2.29 cm

The object is to be placed at a distance of 2.29 cm to the left side of the objective.