Question

A converging mirror is placed on the right hand side of a converging lens as shown in the figure. The focal length of the mirror and the lens are $20cm$ and $15cm$, respectively. The separation between the lens and the mirror is $40cm$ and their principal axis coincide. A point source is placed on the principal axis at a distance $d$ to the left of the lens. If the final beam comes out parallel to the principal axis, then the value of $d$ is

• A. 4 cm
• B. 8 cm
• C. 12 cm
• D. 16 cm

Answer 1

Answer: (C)

Image of lens will act as object for mirror.
Here, $v_1+u_2=40cm$
Lens formula, $\frac{1}{f_1}=\frac{1}{u_1}-\frac{1}{v_1}$
Mirror formula, $\frac{1}{f_2}=\frac{1}{u_2}+\frac{1}{v_2}$
For final image, $v_2=\infty$
So, $\frac{1}{f_2}=\frac{1}{u_2}$
$\Rightarrow u_2=15cm$
Now, $v_1=40-15=25cm$
So, value of $u_1$ should be
$\frac{1}{20}=\frac{1}{u_1}-\frac{1}{25}\Rightarrow \frac{1}{u_1}=\frac{1}{20}+\frac{1}{25}$
$u_1=100/9cm\Rightarrow u_1=11.11cm$
$=12cm$