Question

A Galilean telescope is constructed by an objective of focal length $50\text{cm}$ and eye piece of focal length $5\text{cm}$. If the telescope is to focus an object $2\text{m}$ away from the objective, 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,
$f_0=50\text{cm},f_e=-5\text{cm}$

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

Using lens formula,

$\frac{1}{v_0}-\frac{1}{u_0}=\frac{1}{f_0}$

$\Rightarrow \frac{1}{v_0}-\frac{1}{(-200)}=\frac{1}{50}$

$\Rightarrow \frac{1}{v_0}=\frac{1}{50}-\frac{1}{200}=\frac{3}{200}$

$\Rightarrow v_0=66.67\text{cm}$

As the final image is formed at infinity, the image formed by the objective will be at the focus of the eyepiece.


Therefore, for Galilean Telescope,

Tube length $L=|v_0|-|f_e|$

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

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

Why this question? Caution : In the case of telescope being used to see nearby objects, the formula of tube length and magnification gets modified.