Question

The focal length of convex mirror $M_1$ is $20\text{cm}$ and that of concave mirror $M_2$ is $30\text{cm}$. For the object placed at $O$ as shown in the figure, find the distance of the second image $I_2$ from the pole of the mirror $M_2$. Consider first reflection to be at $M_1$.

• A. $60\text{cm}$
• B. $90\text{cm}$
• C. $120\text{cm}$
• D. $150\text{cm}$

Answer 1

The correct option is C $120\text{cm}$


For the mirror $M_1$,
$u_1=-20\text{cm}$
$f_1=+20\text{cm}$

Using the mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$, we have
$\frac{1}{v_1}+\frac{1}{-20}=\frac{1}{+20}$

$\Rightarrow v_1=+10\text{cm}$

For $M_2$
$u_2=-40\text{cm}(\because P_2{I}_1=40\text{cm})$
$f_2=-30\text{cm}$

Using the mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$, we get,
$\frac{1}{v_2}+\frac{1}{-40}=\frac{1}{-30}$
$\Rightarrow v_2=P_2{I}_2=-120\text{cm}$

$\therefore$ image distance from pole of mirror $M_2$ after second reflection is $120\text{cm}$.

$\begin{array}{c}\text{Why this question ?}\\ \text{In the case of a combination of mirrors,}\\ \text{the image formed by first mirror acts}\\ \text{as an object for the second mirror and}\\ \text{the second mirror will form another image.}\end{array}$