First slide

The optical instruments

Question

A compound microscope is used to enlarge an object kept at a distance 0.03m from its 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, find out the distance by which the eye piece of the microscope must be moved to refocus the image.

Difficult

A

9cm away from objective
B

15cm away from objective
C

6cm away from objective
D

21cm away from objective

Solution

From lens formula
$\begin{array}{l} \frac{1}{F} = \frac{1}{v} - \frac{1}{u} \\ \Rightarrow \frac{1}{0.02} = \frac{1}{v} + \frac{1}{0.03} \\ \Rightarrow v = 0.06 m = 6 cm \\ L e t s a y f o c a l l e n g t h o f r e m a i n i n g c o m b i n a t i o n i s f' \\ \frac{1}{0.02} = \frac{1}{0.1} + \frac{1}{f'} \\ \Rightarrow f' = 0.025 m = 2.5 cm \\ T h e n e w p o s i t i o n o f i m a g e b y o b j e c t i v e l e n s i s v' . \\ U \sin g l e n s f o r m u l a, \\ \frac{1}{2.5} = \frac{1}{v'} - \frac{1}{(- 3)} \\ \Rightarrow v' = 15 cm \\ ∴ Eye piece must be moved away from objective by 15 - 6 = 9 cm \end{array}$

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