A compound microscope is used to enlarge an object kept at a distance `0.03m` from cuts objective which consists of serval convex lenses in contact and has focal length `0.03m`. If a lens focal length `0.1m `is removed from the objective, find out the distance by which the eye-piece of the microscope must be moved to refocus the image.

Explanation

Here, `u = - 0.03 m, F = 0.02 m`
where `F` is focal length of several convex lenses in contact
If `v` is distance of image from the objective, then
`(1)/(v) = (1)/(F) + (1)/(u) = (1)/(0.02) + (1)/(-0.03) = (0.03 - 0.02)/(0.02 xx 0.03)`
`v = (0.02 xx 0.03)/(-0.01) = 0.06 m`
When one lens of `F = 0.1m` is removed, the new focal length of objective becomes `F'`, where
`(1)/(F') = (1)/(F) - (1)/(f) = (1)/(0.02) - (1)/(0.1) = (4)/(0.1)`
`F' = (0.1)/(4) = 0.025m`
Let `v'` be the distance of new images from objective lens
`:. (1)/(v') = (1)/(F') + (1)/(u) = (1)/(0.025) + (1)/(-0.03)`
`(1)/(v') = (+ 0.03 - 0.025)/(0.025 xx 0.03)`
`v' = (0.025 xx 0.03)/(0.005) = 0.15 m`
`:.` Distance through which eye piece of microscope should be moved
`= v' - v = 0.15 - 0.06 = 0.09 m`.