Chapter 17, Problem 45A

To determine

The angle that the reflected ray makes with the mirror.

Answer to Problem 45A

The angle made by the reflected ray with the mirror is $48°$ .

Explanation of Solution

Given:

Angle of incidence is $60°$ .

Angle of rotation of the mirror is $18°$ .

The given diagram is shown below:

  

Calculation:

The ray of light strikes a mirror at an angle from the normal line $N_1$ and then mirror rotated clockwise by angle as shown in the below figure:

  

In the above figure, $M_1$ and $M_2$ are initial and final position of the mirror. Similarly, $N_1$ and $N_2$ are the initial and final positions of the normal. $I$ is the incident ray. $R_1$ and $R_2$ are the initial and final reflected rays.

The incident ray makes an angle of $60°$ with normal so when the normal is rotated by $18°$ , then the angle made by the incident ray will be

  $\begin{array}{l}{\theta }_1=60°-18°\\ {\theta }_1=42°\end{array}$

As the angle of reflection is the same as the incident angle, the reflected ray also makes an angle of $42°$ with the same normal.

As the normal is perpendicular to the surface of the mirror, so the angle made by this reflected ray with the surface is

  $90°-42°=48°$

Conclusion:

Hence, the angle made by the reflected ray with the mirror is $48°$ .