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Q.

Find the separation between the objective lens and the eye-piece of the given telescope, which has an objective lens of focal length 50 cm and an eye piece of focal length 5 cm. The least distance of distinct vision is 25 cm and the telescope is focused for distinct vision on a scale 200 cm away.

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a

75 cm

b

60 cm

c

71 cm

d

74 cm

answer is C.

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Detailed Solution

$\begin{array}{l} L = V_{o} + |u_{e}| \\ \frac{1}{V_{0}} - \frac{1}{u_{0}} = \frac{1}{f_{0}}; \frac{1}{V_{e}} - \frac{1}{U_{e}} = \frac{1}{f_{e}} \\ \frac{1}{V_{0}} = \frac{1}{50} - \frac{1}{200}; \frac{1}{- 25} - \frac{1}{u_{e}} = \frac{1}{5} \\ V_{0} = \frac{200}{3} cm; u_{e} = \frac{- 25}{6} \\ L = \frac{200}{3} + \frac{25}{6} \Rightarrow L = 70 .83 = 71 cm \end{array}$

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