A Galilean telescope has an objective lens of focal length $50 cm$ and eyepiece of focal length $5 cm$ . If the telescope is used to focus an object $2 m$ away from the objective lens, what should be the tube length? (Final image is forming at infinity.)

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Solution

Given,
Focal length of objective, $f_{o} = 50 cm$

Focal length of eyepiece, $f_{e} = - 5 cm$

For objective lens.
$u_{0} = - 2 m = - 200 cm$

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

$\Rightarrow \frac{1}{v_{o}} - \frac{1}{- 200} = \frac{1}{50}$

$\Rightarrow \frac{1}{v_{o}} = \frac{1}{50} - \frac{1}{200} = \frac{3}{200}$

$\Rightarrow v_{o} = 66.67 cm$

Tube length,

$L = v_{0} - | f_{e} |$

$L = 66.67 - 5 = 61.67 cm$

Hence, option $(C)$ is correct.

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A Galilean telescope has an objective lens of focal length 50 cm and eyepiece of focal length 5 cm. If the telescope is used to focus an object 2 m away from the objective lens, what should be the tube length? (Final image is forming at infinity.)

Given, Focal length of objective, fo=50 cm Focal length of eyepiece, fe=−5 cm For objective lens. u0=−2 m=−200 cm 1vo−1uo=1fo ⇒1vo−1−200=150 ⇒1vo=150−1200=3200 ⇒vo=66.67 cm Tube length, L=v0−|fe| L= 66.67−5 = 61.67 cm Hence, option (C) is correct.

A Galilean telescope has an objective lens of focal length $50 cm$ and eyepiece of focal length $5 cm$ . If the telescope is used to focus an object $2 m$ away from the objective lens, what should be the tube length? (Final image is forming at infinity.)