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

• A. 6 cm
• B. 9 cm
• C. 12 cm
• D. 15 cm

Answer 1

The correct option is A 6 cm

The given condition will be satisfied only if one source $\left(S_1\right)$ placed on one side such that u < f (i.e. it lies under the focus). The other source $\left(S_2\right)$ 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 $\frac{1}{f}=\frac{1}{-y}-\frac{1}{-x}\Rightarrow \frac{1}{y}=\frac{1}{x}-\frac{1}{f}....\left(i\right)$
If $S_2$ is the object for lens then $\frac{1}{f}=\frac{1}{+y}-\frac{1}{-(24-x)}\Rightarrow \frac{1}{y}=\frac{1}{f}-\frac{1}{(24-x)}....\left(ii\right)$
From equation (i) and (ii)
$\frac{1}{x}-\frac{1}{f}=\frac{1}{f}-\frac{1}{(24-x)}\Rightarrow \frac{1}{x}+\frac{1}{(24-x)}=\frac{2}{f}=\frac{2}{9}\Rightarrow x^2-24x+108=0$
On solving the equation x =18 cm, 6 cm