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 [2016]

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Solution

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 [2016]

1 50.0 cm

2 54.0 cm

3 37.3 cm

4 46.0 cm

Ans.
(2)

Here $f_{o} = 40 cm,$ $f_{e} = 4 cm$

Tube length $(l)$ = Distance between lenses = $v_{o} + f_{e}$

For objective lens,

$u_{o} = - 200 cm, v_{o} = ?$

$\frac{1}{v_{o}} - \frac{1}{u_{o}} = \frac{1}{f_{o}} or \frac{1}{v_{o}} - \frac{1}{- 200} = \frac{1}{40}$

or $\frac{1}{v_{o}} = \frac{1}{40} - \frac{1}{200} = \frac{4}{200} ∴ v_{o} = 50 cm$

$∴ l = 50 + 4 = 54$ $cm$

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