Optics Question 908
Question: In a concave mirror experiment, an object is placed at a distance $ x _{1} $ from the focus and the image is formed at a distance $ x _{2} $ from the focus. The focal length of the mirror would be
[MP PET 1997]
Options:
A) $ x _{1}x _{2} $
B) $ \sqrt{x _{1}x _{2}} $
C) $ \frac{x _{1}+x _{2}}{2} $
D) $ \sqrt{\frac{x _{1}}{x _{2}}} $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ u=(f+x _{1}) $ and $ v=(f+x _{2}) $
The focal length $ f=\frac{uv}{u+v}=\frac{(f+x _{1})(f+x _{2})}{(f+x _{1})+(f+x _{2})} $
On solving, we get $ f^{2}=x _{1}x _{2} $ or $ f=\sqrt{x _{1}x _{2}} $
