Question

A telescope has an objective lens of focal length $150\, cm$ and an eyepiece of focal length $5\, cm$. If a $50 \,m$ tall tower at a distance of $1\, km$ 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
$\frac{\theta}{\theta_{0}} \approx \frac{\tan \theta}{\tan \theta_{o}}=\frac{\tan \theta}{50 / 1000}=\frac{150}{5} \Rightarrow \tan \theta$