Question

A telescope has an objective lens of focal length $150cm$ and an eyepiece of focal length $5cm$. If a $50m$ tall tower at a distance of $1km$ is observed through this telescope in normal setting, the angle formed by the image of the tower is $\theta$, then $\theta$ is close to :

• A. $1^{\circ }$
• B. $15^{\circ }$
• C. $30^{\circ }$
• D. $60^{\circ }$

Answer 1

Answer: (D)

For normal setting,
Magnifying power $=\frac{f_o}{f_e}=\frac{\theta }{{\theta }_o}$
Where $\theta$ is the angle subtended by the image and ${\theta }_0$ is the angle subtended in the absence of the instrument
$\frac{\theta }{{\theta }_0}\approx \frac{\tan \theta }{\tan {\theta }_o}=\frac{\tan \theta }{50/1000}=\frac{150}{5}\Rightarrow \tan \theta$