Question

A telescope is used to view the moon. What is the angle subtended by the moon at the telescope, if the focal length of objective lens of the telescope is $12\text{cm}$ and the size of the image of the moon formed by the objective is $2\text{cm}?$

• A. ${2.77}^{\circ }$
• B. ${3.77}^{\circ }$
• C. ${4.77}^{\circ }$
• D. ${5.77}^{\circ }$

Answer 1

The correct option is C ${4.77}^{\circ }$

$f_0=12\text{cm}$
Size of the image $h=1\text{cm}$


Let $\theta$ be the angle subtended by moon on the telescope.
Angle subtended by its image will also be $\theta$, as shown in the diagram.
From the diagram,
$\tan \theta =\frac{h}{f_0}$
as $\theta$ is small, $\tan \theta \approx \theta$
$\therefore \frac{h}{f_0}=\frac{1}{12}\text{rad}\approx {4.77}^{\circ }$

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