Question

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

• A. $66.67\text{cm}$
• B. $45\text{cm}$
• C. $61.67\text{cm}$
• D. $71.67\text{cm}$

Answer 1

The correct option is C $61.67\text{cm}$

Given,
Focal length of objective, $f_o=50\text{cm}$

Focal length of eyepiece, $f_e=-5\text{cm}$

For objective lens.
$u_0=-2\text{m}=-200\text{cm}$

$\frac{1}{v_o}-\frac{1}{u_o}=\frac{1}{f_o}$

$\Rightarrow \frac{1}{v_o}-\frac{1}{-200}=\frac{1}{50}$

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

$\Rightarrow v_o=66.67\text{cm}$

Tube length,

$L=v_0-|f_e|$

$L=66.67-5=61.67\text{cm}$

Hence, option $\left(C\right)$ is correct.