Optics Question 809
Question: Two point source $ S _{1} $ and $ S _{2} $ are 24 cm apart. Where a convex lens of focal length 9 cm should be placed in between them so that the images of both sources are formed at the same place?
Options:
A) 6 cm from $ S _{1} $
B) 15 cm from $ S _{1} $
C) 10 cm from $ S _{1} $
D) 12 cm from $ S _{1} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] In this case, one of the image will be real and the other virtual.
Let us assume that image of $ S _{1} $ is real and that of $ S _{2} $ is virtual.
Applying $ \frac{1}{v}-\frac{1}{u}=\frac{1}{f} $ F
or $ S _{1}:\frac{1}{y}+\frac{1}{x}=\frac{1}{9} $ ..(i)
For $ S _{2}:\frac{1}{y}+\frac{1}{24-x}=\frac{1}{9} $ -(ii)
Solving eqs. (i) and (ii), we get $ x=6cm $
