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Q.

The focal lengths of the objective and the eyepiece of a compound microscope are 2.0cm and 3.0cm respectively. The distance between the objective and the eyepiece is 15.0cm. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance (in cm) of the object and the image produced by the objective measured from the objective lens are respectively.

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a

2.4 and 15.0

b

2.0 and 3.0

c

2.0 and 12.0

d

2.4 and 12.0

answer is A.

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Detailed Solution

When final image is formed at infinity.
Length of the tube $= v_{0} + f_{e}$
$= 15 = v_{0} + 3 \Rightarrow v_{0} = 12 c m$
For objective lens $\frac{1}{f_{0}} = \frac{1}{v_{0}} - \frac{1}{u_{0}}$
$\Rightarrow \frac{1}{(+ 2)} = \frac{1}{(+ 12)} - \frac{1}{u_{0}} \Rightarrow u_{0} = - 2.4 c m$

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