Optics Question 125
Question: Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place
Options:
A) 6 cm
B) 9 cm
C) 12 cm
D) 15 cm
Show Answer
Answer:
Correct Answer: A
Solution:
The given condition will be satisfied only if one source (S1) placed on one side such that u < f (i.e. it lies under the focus).
The other source (S2) is placed on the other side of the lens such that u > f (i.e. it lies beyond the focus).
If $ S _{1} $ is the object for lens then $ \frac{1}{f}=\frac{1}{-y}-\frac{1}{-x} $
$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{x}-\frac{1}{f} $ …..(i) If $ S _{2} $ is the object for lens then $ \frac{1}{f}=\frac{1}{+y}-\frac{1}{-(24-x)} $
$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{f}-\frac{1}{(24-x)} $ …..(ii) From equation (i) and (ii) $ \frac{1}{x}-\frac{1}{f}=\frac{1}{f}-\frac{1}{(24-x)} $
$ \Rightarrow $ $ \frac{1}{x}+\frac{1}{(24-x)}=\frac{2}{f}=\frac{2}{9} $
$ \Rightarrow $ $ x^{2}-24x+108=0 $ . After solving the equation $ x=18\ cm $ , 6 cm.
