Optics Question 817
Question: A luminous object and a screen are at a fixed distance D apart. A converging lens of focal length l is placed between the object and screen. A real image of the object in formed on the screen for two lens positions of they are separated by a distance d equal to
Options:
A) $ \sqrt{D( D+4f )} $
B) $ \sqrt{D( D-4f )} $
C) $ \sqrt{2D( D-4f )} $
D) $ \sqrt{D^{2}+4f} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let the object distance be x. Then, the image distance is $ D-x $ .
From lens equation, $ \frac{1}{x}+\frac{1}{D-x}=\frac{1}{f} $
On algebraic rearrangement, we get $ x^{2}-Dx+Df=0 $
On solving for x, we get $ x _{1}=\frac{D-\sqrt{D( D-4f )}}{2}\text{ }x _{2}=\frac{D+\sqrt{D( D-4f )}}{2} $
The distance between the two object positions is $ d=x _{2}-x _{1}=\sqrt{D( D-4f )} $
