If an observer is walking away from the plane mirrorr with `6m//sec` . Then the velocity of the image with respect to observer will be

Options

A. 6 m/sec
B. - 6 m/sec
C. 12 m/sec
D. 3 m/sec

Answer

To solve the problem, we need to determine the velocity of the image with respect to the observer who is walking away from a plane mirror at a speed of 6 m/s.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The observer is moving away from the plane mirror at a velocity of 6 m/s.
- In a plane mirror, the image distance is equal to the object distance. Therefore, as the observer moves away from the mirror, the image also appears to move away from the mirror.

2. **Assigning Velocities**:
- Let \( V_{OP} \) be the velocity of the observer with respect to the plane mirror. Since the observer is moving away from the mirror, we can assign this a negative value:
\[ V_{OP} = -6 \text{ m/s} \]

3. **Image Velocity**:
- The image will move away from the mirror with the same speed as the observer but in the opposite direction (towards the right). Thus, the velocity of the image with respect to the mirror \( V_{IP} \) is:
\[ V_{IP} = 6 \text{ m/s} \]

4. **Finding the Relative Velocity of the Image with Respect to the Observer**:
- The relative velocity of the image with respect to the observer \( V_{IO} \) can be calculated using the formula:
\[ V_{IO} = V_{IP} - V_{OP} \]
- Substituting the values:
\[ V_{IO} = 6 - (-6) = 6 + 6 = 12 \text{ m/s} \]

5. **Conclusion**:
- The velocity of the image with respect to the observer is \( 12 \text{ m/s} \).

### Final Answer:
The velocity of the image with respect to the observer is **12 m/s**.