Question

Two plane mirrors $M_1$ and $M_2$ each have length $1\text{m}$ and are separated by $1\text{cm}$. A ray of light is incident on one end of mirror $M_1$ at an angle of ${45}^{\circ }$. How many reflections will the ray have before going out from the other end?

• A. $50$
• B. $51$
• C. $100$
• D. $101$

Answer 1

The correct option is D $101$


Here $\text{tan}{45}^o=\frac{\text{BC}}{\text{AC}}=1$
$\Rightarrow \text{BC}=\text{AC}=1\text{cm}$
So each reflection occures after $1\text{cm}$

Reflection will occur at $x=0,2,4,...\text{cm}$ from mirror $M_1$ and $x=1,3,5,...\text{cm}$ from mirror $M_2$.
Hence the total reflections will be $x=0,1,\mathrm{2...100}$
which are total 101 reflections
Hence, the correct answer is option (d).

Why this question? Concept: Number of images formed in two parallel mirror are infinite because an image formed by one mirror can act as an object for the second mirror. And every image formed by the second mirror can act as an object for the first mirror. This image formation will continue for both the mirrors.