Question

For an astronomical telescope, the angular size of object is $0.1\text{rad}$ and the angular size of image is $0.2\text{rad}$. If the objective lens has focal length $100\text{cm}$ then the distance of image formed by the objective lens from the eyepiece is -

• A. $20\text{cm}$
• B. $30\text{cm}$
• C. $40\text{cm}$
• D. $50\text{cm}$

Answer 1

The correct option is D $50\text{cm}$

Given:
$\alpha =0.1\text{rad}$
$\beta =0.2\text{rad}$
$f_o=100\text{cm}$


We know that, magnifying power of a telescope is,

$m=\frac{\beta }{\alpha }=\frac{f_o}{|u_e|}$

$\Rightarrow \frac{0.2}{0.1}=\frac{100}{|u_e|}$

$\Rightarrow |u_e|=50\text{cm}$

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