Question

Two plane mirrors are inclined at $ {70}^{\circ }$. A ray incident on one mirror at an angle $ \theta $, after reflection, falls on the second mirror and is reflected from there parallel to the first mirror. The value of $ \theta $ is:

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${55}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is D

${50}^{\circ }$

Let, the angle between the mirror $M_2$, and the ray is $\alpha$.

Step 1: Calculation of the angle between the mirror $M_2$, and the ray

$\alpha +{20}^{\circ }={90}^{\circ }$

Here, $\alpha$ is the angle between the mirror $M_2$ and the ray.

$$\begin{gathered} \alpha ={90}^{\circ }-{20}^{\circ } \\ \alpha ={70}^{\circ } \end{gathered}$$

Step 2: Calculation of the incident angle $\left(\theta \right)$.

The summation of the three angles of a triangle is ${180}^{\circ }$.

$$\begin{gathered} {70}^{\circ }+{70}^{\circ }+\left({90}^{\circ }-\theta \right)={180}^{\circ } \\ \theta ={230}^{\circ }-{180}^{\circ } \\ \theta ={50}^{\circ } \end{gathered}$$

Therefore, the incident angle is ${50}^{\circ }$.

Hence, option (D) is correct.