A plane mirror and a person are moving towards each other with same velocity v. Then the velocity of the image is

Options

A. v
B. 2v
C. 3v
D. 4v

Explanation

To solve the problem of finding the velocity of the image when a plane mirror and a person are moving towards each other with the same velocity \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a plane mirror and a person (the object) moving towards each other.
- Both the mirror and the person are moving with the same speed \( v \).

2. **Identifying the Image Formation**:
- The image formed by a plane mirror is located at the same distance behind the mirror as the object is in front of it.
- If the object (the person) is at a distance \( u \) from the mirror, the image will be at a distance \( u' = u \) behind the mirror.

3. **Using the Concept of Relative Velocity**:
- As the person moves towards the mirror with velocity \( v \), the distance \( u \) is decreasing.
- The velocity of the object towards the mirror is \( -v \) (negative because the distance is decreasing).

4. **Considering the Mirror's Motion**:
- The mirror is also moving towards the person with velocity \( v \).
- Therefore, the effective distance between the person and the image is decreasing at a rate that combines both velocities.

5. **Calculating the Velocity of the Image**:
- The velocity of the image \( v_i \) can be determined by considering both the motion of the object and the motion of the mirror.
- The image moves away from the mirror at the same rate that the mirror moves towards the object plus the rate at which the object approaches the mirror.

6. **Final Calculation**:
- The total velocity of the image \( v_i \) is given by:
\[ v_i = v + v = 2v \]
- Thus, the velocity of the image is \( 2v \).

### Conclusion:
The velocity of the image is \( 2v \).