An astronomical telescope has objective and eyepiece of focal length 40 cm and 5 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:

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46.0 cm

37.3 cm

55.0 cm

50.0 cm

answer is D.

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Detailed Solution

Using lens formula for objective lens
$\begin{array}{l} \frac{1}{v_{u}} - \frac{1}{u_{0}} = \frac{1}{f_{0}} \\ \frac{1}{v_{0}} = \frac{1}{u_{0}} + \frac{1}{f_{0}} \\ \frac{1}{v_{0}} = \frac{1}{40} - \frac{1}{200} \\ \frac{5 - 1}{500} = V_{0} = 50 c m \end{array}$
Tube length $l = |v_{0}| + f_{e}$
= 50 + 5 = 55 cm

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