Optics Question 79
Question: A concave mirror of focal length $ 100cm $ is used to obtain the image of the sun which subtends an angle of $ 30{}^\circ . $ The diameter of the image of the sun will be
Options:
A) $ 1.74cm $
B) $ 0.87cm $
C) $ 0.435cm $
D) $ 100cm $
Show Answer
Answer:
Correct Answer: B
Solution:
The angle subtended by the image of the sun at the mirror $ =3{0}’={{( \frac{1}{2} )}^{o}}=\frac{\pi }{360}rad $ .
If $ x $ be the diameter of the image of the sun, then $ \frac{Arc}{Radius}=\frac{x}{100}=\frac{1}{2}.\frac{2\pi }{360}=\frac{\pi }{360} $
$ \Rightarrow x=\frac{100\pi }{360}=0.87cm $
