A light ray strikes a horizontal plane mirror and gets deviated by `pi//3`. By what angle should the mirror be tilted so that the reflected ray becomes vertical?

Options

A. `pi//6`
B. `(pi)//2`
C. `(pi)/3`
D. `(pi)//4`

Answer

To solve the problem, we need to determine the angle by which the mirror should be tilted so that the reflected ray becomes vertical after initially being deviated by \(\frac{\pi}{3}\).

### Step-by-Step Solution:

1. **Understand the Initial Setup**:
- A light ray strikes a horizontal plane mirror and is deviated by an angle of \(\frac{\pi}{3}\) (or 60 degrees). This means that the angle of reflection is also \(\frac{\pi}{3}\) due to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

2. **Determine the Angle of Incidence**:
- Let the angle of incidence be \(i\). According to the law of reflection:
\[ i = \frac{\pi}{3} \]
- The angle between the incident ray and the normal (which is vertical in this case) is:
\[ \text{Angle with normal} = \frac{\pi}{2} - i = \frac{\pi}{2} - \frac{\pi}{3} = \frac{\pi}{6} \]

3. **Determine the Required Angle for Vertical Reflection**:
- For the reflected ray to become vertical, the angle of reflection must be \(0\) with respect to the vertical axis. This means that we need to adjust the angle of incidence such that the reflected ray is directed straight up.

4. **Tilt the Mirror**:
- If we tilt the mirror by an angle \(\theta\), the angle of incidence will change. The new angle of incidence will be:
\[ i' = i + \theta \]
- The new angle of reflection will also be equal to the new angle of incidence:
\[ r' = i' = i + \theta \]
- For the reflected ray to be vertical, we need:
\[ r' = 0 \Rightarrow i + \theta = 0 \Rightarrow \theta = -i \]
- Since \(i = \frac{\pi}{3}\), we have:
\[ \theta = -\frac{\pi}{3} \]

5. **Calculate the Total Tilt**:
- However, we are looking for the angle by which the mirror should be tilted to achieve this condition. Since the original angle of incidence was \(\frac{\pi}{3}\), we need to tilt the mirror by an angle that compensates for this deviation:
\[ \text{Tilt angle} = \frac{\pi}{6} \]

### Final Answer:
The mirror should be tilted by \(\frac{\pi}{6}\) (or 30 degrees) so that the reflected ray becomes vertical.