Question

The reflecting surfaces of two mirrors $M_1$ and $M_2$ are at an angle $\theta ($ 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 $\varphi$ Then,

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

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 $\Delta ACD,2i_1+2i_2+\varphi =180^{\circ }$
$\varphi =180^{\circ }-2\left(i_1+i_2\right)=180^{\circ }-2\theta$ (Using (i))