Question

The focal lengths of the objective and eye-piece of a telescope are respectively $100cm$ and $2cm$. The moon subtends an angle of ${0.5}^{\circ }$ at the eye. If it is looked through the telescope, the angle subtended by the moon’s image will be

• A. ${100}^{\circ }$
• B. ${50}^{\circ }$
• C. ${25}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

The correct option is C ${25}^{\circ }$

$f_0=100cm$
$f_e=2cm$

Angular magnification of telescope

$m=\frac{{\theta }_i}{{\theta }_o}=\frac{f_o}{f_e}$ where ${\theta }_o$ is the angle subtended by the object at the eye and ${\theta }_i$ is the angle subtended by the final image at the eye.

$\Rightarrow \frac{-100}{2}=\frac{{\theta }_i}{{0.5}^0}$
$\Rightarrow {\theta }_i=-{25}^0$ where the minus sign indicates the direction in which we measure the angle.