A compound microscope is used to enlarge an object kept at a distance `0.03m` from uuts 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

`(1)/(v_(0)) - (1)/(-0.03) = (1)/(0.02) rArr (1)/(v_(0)) = (1)/(0.02) - (1)/(0.03) = (3-2)/(0.06)`
`v_(0) = 0.06m`
When alens of focal length `0.1m` is removed, new focal length of objective
`(1)/(F') = (1)/(F)-(1)/(0.1) =1/0.02-1/0.1=(1-1.02)/0.02=0.8/0.02=1/0.025`
`(1)/(v'_(0)) - (1)/(-0.03) = (1)/(F') = (1)/(0.025)`
`(1)/(v'_(0)) = (1)/(0.025)- (1)/(0.030) = (3-2.5)/(0.075) = (0.5)/(0.075) = (1)/(0.15)`
`v'_(0) = 0.15cm`
Shift of eye-piece `= v'_(0)-v_(0) = 0.015-0.06=0.09m`
`= 9cm`