Question

Consider the following system. Assuming that the first image is formed after reflection from mirror $M_1$, the $x-$co-ordinate of the final image formed by reflection from the mirror $M_2$, if $P_2$ is taken as origin will be

• A. $\frac{-300}{23}\text{cm}$
• B. $\frac{-300}{32}\text{cm}$
• C. $\frac{+300}{23}\text{cm}$
• D. $\frac{+300}{32}\text{cm}$

Answer 1

The correct option is C $\frac{+300}{23}\text{cm}$

For first reflection at mirror $M_1$,
$u=-15\text{cm}$
$f=-10\text{cm}$
So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{15}=\frac{-1}{10}$
$\Rightarrow \frac{1}{v}=\frac{-1}{30}$
$\Rightarrow v=-30\text{cm}$
This first image will act as the object for the mirror $M_2$.
For second reflection at mirror $M_2$,
$u=-(130-30)=-100\text{cm}$
$f=+15\text{cm}$
So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{100}=\frac{1}{15}$
$\Rightarrow \frac{1}{v}=\frac{23}{300}$
$\Rightarrow v=\frac{300}{23}\text{cm}$
Thus, the $x-$ co-ordinate of the final image is $\frac{300}{23}\text{cm}$