A plane mirror reflecting a ray of incident light is rotated through an angle of `30^@` about an axis through the point of incidence in the plane of the mirror and perpendicular to the plane of incidence then

Options

A. the incident ray is fixed
B. the reflected ray rotates through an angle `theta`
C. the reflected ray rotates through an angle `theta//2`
D. the reflected ray rotates through an angle of `2theta`

Answer

To solve the problem of how much the reflected ray rotates when a plane mirror is rotated through an angle of \(30^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a plane mirror and an incident ray of light striking the mirror.
- The mirror is rotated through an angle of \(30^\circ\) about an axis that is perpendicular to the plane of incidence.

2. **Identify the Angle of Rotation**:
- The angle through which the mirror is rotated is given as \(30^\circ\). This is denoted as \( \omega = 30^\circ \).

3. **Determine the Effect on the Reflected Ray**:
- According to the laws of reflection, when a plane mirror is rotated, the angle of the reflected ray changes. Specifically, the change in the angle of the reflected ray is twice the angle through which the mirror is rotated.
- Therefore, if the mirror rotates by \( \omega \), the reflected ray will rotate by \( 2\omega \).

4. **Calculate the Total Rotation of the Reflected Ray**:
- Since \( \omega = 30^\circ\), the rotation of the reflected ray will be:
\[ \text{Rotation of reflected ray} = 2 \times \omega = 2 \times 30^\circ = 60^\circ \]

5. **Conclusion**:
- The reflected ray will rotate through an angle of \(60^\circ\) when the plane mirror is rotated through an angle of \(30^\circ\).

### Final Answer:
The reflected ray rotates through an angle of \(60^\circ\).

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