Optics Question 606
Question: A lens is placed between a source of light and a wall. It forms images of area $ A _{1} $ and $ A _{2} $ on the wall for its two different positions. The area of the source or light is
[CBSE PMT 1995]
Options:
A) $ \frac{A _{1}+A _{2}}{2} $
B) $ {{[ \frac{1}{A _{1}}+\frac{1}{A _{2}} ]}^{-1}} $
C) $ \sqrt{A _{1}A _{2}} $
D) $ {{[ \frac{\sqrt{A _{1}}+\sqrt{A _{2}}}{2} ]}^{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ m _{1}=\frac{A _{1}}{O} $ and $ m _{2}=\frac{A _{2}}{O} $
$ \Rightarrow m _{1}m _{2}=\frac{A _{1}A _{2}}{O _{2}} $ .
Also it can be proved that $ m _{1}m _{2}=1 $ .
So $ O=\sqrt{A _{1}A _{2}} $
