The focal length of objective and eyepiece of an astronomical telescope are 25 cm and 2.5 cm respectively. The telescope is focused on an object 1.5 m from objective, the final image is at 25 cm from the eye of the observer. Calculate the length of the telescope.

Solution

Here given an astronomical telescope.

$Focal length of the objective, f_{0} = 25 cm F o c a l l e n g t h o f e y e p i e c e, f_{e} = 2.5 cm$

$Object distance, u_{0} = - 1.5 m = - 150 cm, Distance of image from eyepiece, v_{e} = 25 cm$

From the formula,
$\frac{1}{v_{0}} - \frac{1}{u_{0}} = \frac{1}{f_{0}}$

$\frac{1}{v_{0}} = \frac{1}{f_{0}} + \frac{1}{u_{0}} = \frac{1}{25} - \frac{1}{150} = \frac{5}{150} = \frac{1}{30}$

i.e., $v_{0} = 30 cm .$
which is the required distance from the objective.
Now, again using the formula,
$\frac{1}{v_{e}} - \frac{1}{u_{e}} = \frac{1}{f_{e}}$

$\Rightarrow$ $- \frac{1}{u_{e}} = \frac{1}{f_{e}} - \frac{1}{v_{e}}$

$\Rightarrow$ $- \frac{1}{u_{e}} = \frac{1}{2.5} - \frac{1}{25} = \frac{9}{25}$

i.e., $u_{e} = - \frac{25}{9} cm$

Length of the telescope is given by,
$L = v_{0} + |u_{e}| = 30 + \frac{25}{9} = \frac{295}{9} = 32.8 cm .$

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The focal length of objective and eyepiece of an astronomical telescope are 25 cm and 2.5 cm respectively. The telescope is focused on an object 1.5 m from objective, the final image is at 25 cm from the eye of the observer. Calculate the length of the telescope.

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