Question

A telescope is used to view the moon. What is the angle subtended by the moon at the objective lens, if the focal length of the objective lens is $12\text{cm}$ and the size of the image of the moon formed by the objective lens is $1\text{cm}$?

• A. ${2.78}^{\circ }$
• B. ${4.78}^{\circ }$
• C. ${9.78}^{\circ }$
• D. ${6.78}^{\circ }$

Answer 1

The correct option is B ${4.78}^{\circ }$

Given,
$f_0=12\text{cm}$

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


Let, $\theta$ be the angle subtended by the moon on the telescope.
Angle subtended by its image will also be $\theta$.

From the figure,

$\tan \theta =\frac{h}{f_0}$

$\therefore \theta ={\tan }^{-1}\left(\frac{h}{f_0}\right)={\tan }^{-1}\left(\frac{1}{12}\right)$

$\Rightarrow \theta \approx {4.78}^{\circ }$

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

Key Note: Whenever object distance is large compared to focal length of the lenses, object is considered to be at infinity.