Question

The reflecting surfaces of two mirrors $M_{1}$ and $M_{2}$ are at an angle $\theta\left(\right.$ angle $\theta$ between $0^{\circ}$ and $90^{\circ}$ ) as shown in the figure. A ray of light is incident on $M_{1}$. The emerging ray intersects the incident ray at an angle $\phi $ Then,

• A. $\phi=\theta$
• B. $\phi=180^{\circ}-\theta$
• C. $\phi=90^{\circ}-\theta$
• D. $\phi=180^{\circ}-2 \theta$

Answer 1

Answer: (D)

Let $i_{1}$ be the angle of incidence on mirror $M_{1}$ and $i_{2}$ be the angle of incidence on mirror $M_{2}$
In $\Delta ABC$
$90^{\circ}-i_{1}+\theta+90^{\circ}-i_{2}=180^{\circ}$
or $i_{1}+i_{2}=\theta\,\,\,\,\,\,\dots(i)$
In $\Delta \,ACD, 2 i_{1}+2 i_{2}+\phi=180^{\circ}$
$\phi=180^{\circ}-2\left(i_{1}+i_{2}\right)=180^{\circ}-2 \theta$ (Using (i))