Question

Two plane mirrors $L_1$ and $L_2$ are parallel to each other and 3 m apart. A person standing x m from the right mirror $L_2$ looks into this mirror and sees a series of images. The distance between the first and second image is 4 m. Then, the value of x is

• A. 2 m
• B. 1.5 m
• C. 1 m
• D. 2.5 m

Answer 1

Answer: (C)

1 m

$\begin{array}{c}\text{i, is the image of object from}\\ L_2\text{. And,}{i}_2\text{is the image of}\\ \text{object from}{L}_1\text{.}\\ \text{And,}{i}_3\text{is the image due to}{i}_2\\ \text{from}{L}_2\text{.}\end{array}$

$\begin{array}{c}\text{According to question}\\ \text{distance between}{i}_3\text{\&}{i}_1=4m\\ \begin{array}{cc}6-x& -x=4\\ \Rightarrow 2x& =2\Rightarrow x=1m\\ \therefore x& =1m\end{array}\end{array}$