Question

Two points sources $S_1$ and $S_2$ are $24cm$ apart. Where should a convex lens of focal length $9cm$ be placed in between them so that the images of both sources are formed at the same place?

• A. $6cm$ from $S_1$
• B. $15cm$ from $S_1$
• C. $10cm$ from $S_1$
• D. $12cm$ from $S_1$

Answer 1

The correct option is A $6cm$ from $S_1$

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 $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
For $S_1:\frac{1}{y}+\frac{1}{x}=\frac{1}{9}....\left(i\right)$
For $S_2:\frac{1}{y}+\frac{1}{24-x}=\frac{1}{9}....\left(ii\right)$
Solving Eqs. (i) and (ii), we get
$x=6cm$.