Question

A point source of light is placed in front of a plane mirror as shown in the figure. Determine the length of the reflected path of light on the screen $\left(\Sigma \right)$.

• A. $L$
• B. $2L$
• C. $\frac{3L}{2}$
• D. $\frac{L}{2}$

Answer 1

The correct option is C $\frac{3L}{2}$


From the ray diagram, we can write that,
$△SOP$ and $△RMP$ are similar

$\therefore \frac{SO}{OP}=\frac{RM}{MP}\Rightarrow RM=MP=2L$

Also, $△STQ$ and $△QMX$ are similar

So, $\frac{ST}{TQ}=\frac{2L}{L}=\frac{QM}{MX}$
$\Rightarrow MX=\frac{L}{2}$

Therefore, length of the reflected path of light on the screen

$RX=RM-MX=\frac{3L}{2}$

$\begin{array}{c}\text{Why this Question}?\\ \text{This question will help you to build conceptual understanding of ray diagram.}\\ \text{It also helps you to understand how to use the concept of similar triangles to achieve the final answer.}\\ \\ \text{Note :- Condition of similarity of triangles:}\\ \text{1. Corresponding angles of both the triangles are equal.}\\ \text{2. Corresponding sides of both the triangles are in proportion to each other.}\end{array}$