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

Options

A. The reflected ray does not rotate
B. The reflected ray rotates through an angle `theta`
C. The reflected ray rotates through an angle `2 theta`
D. The incident ray is fixed

Answer

To solve the problem of a plane mirror reflecting a ray of incident light that is rotated through an angle θ, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Setup**:
- Consider a plane mirror positioned vertically. A ray of light strikes the mirror at an angle φ with respect to the normal (the line perpendicular to the surface of the mirror).
- According to the law of reflection, the angle of incidence (φ) is equal to the angle of reflection (φ).

2. **Identify the Rotation of the Mirror**:
- The mirror is rotated through an angle θ about an axis that passes through the point of incidence and is perpendicular to the plane of incidence.
- This rotation changes the orientation of the mirror but does not change the point of incidence.

3. **Determine the New Angle of Reflection**:
- After the mirror is rotated, the normal to the mirror at the point of incidence also rotates. The new angle of the normal with respect to the original position is now θ.
- Therefore, the angle between the incident ray and the new normal is now φ + θ.

4. **Calculate the New Angle of Reflection**:
- Since the angle of incidence is now φ + θ, the angle of reflection will also be φ + θ (by the law of reflection).

5. **Determine the Total Deviation of the Reflected Ray**:
- The deviation (Δ) of the reflected ray can be calculated as the difference between the original angle of reflection and the new angle of reflection.
- The original angle of reflection was φ, and the new angle of reflection is φ + θ.
- Therefore, the total deviation is given by:
\[ \Delta = (\phi + \theta) - \phi = \theta \]

### Final Answer:
The deviation of the reflected ray when the mirror is rotated through an angle θ is **θ**.