There are two plane mirror with reflecting suface faciing each other.The mirrors are moving with speed v away form each other .A point object is placed between the mirrors.The velocity of the n-th image will be

Options

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

Explanation

To solve the problem of finding the velocity of the n-th image formed by two plane mirrors moving away from each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors facing each other, and they are moving away from each other with a speed \( v \).
- A point object is placed between the mirrors.

2. **Assuming the Motion**:
- For simplicity, we can assume one mirror is stationary and the other is moving away with speed \( v \). This does not change the relative motion between the mirrors.

3. **Finding the Velocity of the First Image**:
- The first image of the object formed by the moving mirror will appear to be at a distance equal to the distance of the object from the mirror.
- Since the mirror is moving away with speed \( v \), the image will also move away from the object at a speed of \( 2v \) (the object is stationary, and the image moves at the same speed as the mirror, plus the distance from the object).

4. **Finding the Velocity of the Second Image**:
- The second image is formed by the reflection of the first image in the opposite mirror.
- Since the first image is moving away from the stationary mirror at \( 2v \), the second image will move away from the first mirror at a speed of \( 2 \times 2v = 4v \).

5. **Generalizing for the n-th Image**:
- Continuing this pattern, we can see that the velocity of the n-th image can be expressed as:
\[ v_n = 2^n v \]
- This means that the velocity of the n-th image is \( 2^n v \).

6. **Final Expression**:
- Therefore, the velocity of the n-th image formed by the two mirrors moving away from each other is:
\[ v_n = 2nv \]
- This matches our earlier deductions and confirms that the velocity of the n-th image is indeed \( 2nv \).

### Conclusion:
The velocity of the n-th image is \( 2nv \).

---