If the reflected ray is rotated by an angle of `4theta` in clockwisse direction then the mirror was rotated by

Options

A. `2theta` in anti-clockwise direction
B. `4theta` in anti-clockwise direction
C. `2theta` in clockwise direction
D. `4theta` in clockwise direction

Explanation

To solve the problem, we need to understand the relationship between the rotation of a mirror and the rotation of the reflected ray.

### Step-by-Step Solution:

1. **Understand the relationship**: When a plane mirror is rotated by an angle \( \alpha \), the angle of the reflected ray changes by \( 2\alpha \). This is a fundamental property of reflection in optics.

2. **Identify the given information**: According to the problem, the reflected ray is rotated by an angle of \( 4\theta \) in the clockwise direction.

3. **Set up the equation**: Since the reflected ray rotates by \( 2\alpha \), we can set up the equation:
\[ 2\alpha = 4\theta \]

4. **Solve for \( \alpha \)**: To find the angle by which the mirror was rotated, we divide both sides of the equation by 2:
\[ \alpha = \frac{4\theta}{2} = 2\theta \]

5. **Determine the direction of rotation**: The problem states that the reflected ray is rotated in the clockwise direction. Since the mirror's rotation is opposite to the direction of the reflected ray's rotation, the mirror must be rotated in the anticlockwise direction.

6. **Conclusion**: Therefore, the mirror was rotated by \( 2\theta \) in the anticlockwise direction.

### Final Answer:
The mirror was rotated by \( 2\theta \) in the anticlockwise direction.

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