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Telescopes

The optical l...

Question

The optical length of an astronomical telescope with magnifying power of 10, for normal vision is 44cm. What is focal length of the objective?

A

40cm

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B

22cm

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C

10cm

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D

4cm

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Solution

The correct option is A 40cm
Length of telescope $L = f_{o} + f_{e}$
$∴$ $f_{o} + f_{e} = 44$
We get $f_{e} = 44 - f_{o}$
Magnification of astronomical telescope for normal vision $| M | = \frac{f_{o}}{f_{e}}$
OR $10 = \frac{f_{o}}{44 - f_{o}}$
OR $440 - 10 f_{o} = f_{o}$
$⟹$ $f_{o} = \frac{440}{11} = 40$ cm

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