Optics Question 129

Question: A compound microscope is used to enlarge an object kept at a distance 0.03m from it’s objective which consists of several convex lenses in contact and has focal length 0.02m. If a lens of focal length 0.1m is removed from the objective, then by what distance the eye-piece of the microscope must be moved to refocus the image

Options:

A) 2.5 cm

B) 6 cm

C) 15 cm

D) 9 cm

Show Answer

Answer:

Correct Answer: D

Solution:

If initially the objective (focal length Fo) forms the image at distance vo then vo=uofouofo=3×232=6cm

Now as in case of lenses in contact 1Fo=1f1+1f2+1f3+..=1f1+1Fo

1v2(15)=(12)10

So if one of the lens is removed, the focal length of the remaining lens system 1Fo=1F01f1=12110

Therefore Fo=2.5cm

This lens will form the image of same object at a distance vo such that vo=uoFouoFo=3×2.5(32.5)=15cm

So to refocus the image, eye-piece must be moved by the same distance through which the image formed by the objective has shifted i.e. 15 ? 6 = 9 cm.



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