Optics Question 832
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 :
Options:
A) 6.1 rad
B) 3.2 rad
C) 1.5 rad
D) 0.2 rad
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Magnifying power of telescope, $ MP=\frac{\beta ( \text{angle subtended by image at eye piece} )}{\alpha ( \text{angle subtended by object on objective} )} $ Also, $ MP=\frac{f _{0}}{f _{e}}=\frac{150}{5}=30\text{ }\alpha =\frac{50}{1000}=\frac{1}{20}rad $
$ \therefore \beta =\theta =MP\times \alpha =30\times \frac{1}{20}=\frac{3}{2}=1.5rad $
