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  4. An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance :

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Q. An astronomical telescope has objective and eyepiece of focal lengths $40\, cm$ and $4 \,cm$ respectively. To view an object $200\, cm$ away from the objective, the lenses must be separated by a distance :

NEETNEET 2016Ray Optics and Optical Instruments

Solution:

Using lens formula for objective lens
$\frac{1}{v_{0} } -\frac{1}{u_{0}} = \frac{1}{f_{0}} \Rightarrow \frac{1}{v_{0}} = \frac{1}{f_{0}} + \frac{1}{u_{0}} $
$ \Rightarrow \frac{1}{v_{0}} = \frac{1}{40} + \frac{1}{-200} = \frac{+5-1}{200} $
$ \Rightarrow v_{0} = 50 cm$
Tube length $\ell = \left|\text{v}_{0}\right| + f_{e} = 50 + 4 = 54 \; cm $