Two plane mirrors are placed parallel to each other at a distance L apart.A point object O placed between them, at a distance `L/3` from one mirror.Both mirrors form multiple images.The distance between any two images cannot be

Options

A. `(3L)/(2)`
B. `(2L)/(3)`
C. `2L`
D. None of these

Answer

To solve the problem of finding the distance between any two images formed by two parallel mirrors with a point object placed between them, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Setup**:
- We have two plane mirrors (let's call them M1 and M2) placed parallel to each other at a distance \( L \).
- A point object \( O \) is placed between the mirrors at a distance \( \frac{L}{3} \) from mirror M1.

2. **Calculate the Position of the First Image**:
- The first image \( I_1 \) formed by mirror M1 will be at a distance \( \frac{L}{3} \) behind M1. Thus, the position of \( I_1 \) is:
\[ I_1 = -\frac{L}{3} \]

3. **Calculate the Position of the Second Image**:
- The image \( I_1 \) acts as an object for mirror M2. The distance from \( I_1 \) to M2 is \( L + \frac{L}{3} = \frac{4L}{3} \).
- The second image \( I_2 \) formed by mirror M2 will be at a distance \( \frac{4L}{3} \) behind M2:
\[ I_2 = L + \frac{4L}{3} = \frac{7L}{3} \]

4. **Calculate the Position of the Third Image**:
- The image \( I_2 \) acts as an object for mirror M1. The distance from \( I_2 \) to M1 is \( L + \frac{7L}{3} = \frac{10L}{3} \).
- The third image \( I_3 \) formed by mirror M1 will be at:
\[ I_3 = -\left(\frac{10L}{3}\right) = -\frac{10L}{3} \]

5. **Continue Finding Subsequent Images**:
- Continuing this process, we find that the images alternate between the two mirrors, and their positions can be calculated similarly.

6. **Calculate Distances Between Images**:
- The distances between adjacent images can be calculated:
- Distance between \( I_1 \) and \( I_2 \):
\[ d_{12} = I_2 - I_1 = \frac{7L}{3} - \left(-\frac{L}{3}\right) = \frac{8L}{3} \]
- Distance between \( I_2 \) and \( I_3 \):
\[ d_{23} = I_3 - I_2 = -\frac{10L}{3} - \frac{7L}{3} = -\frac{17L}{3} \]

7. **Generalize the Distances**:
- The distances between any two adjacent images can be expressed in the form \( d = \frac{2nL}{3} \) where \( n \) is an integer.
- The possible distances will be multiples of \( \frac{2L}{3} \).

8. **Conclusion**:
- Since the distances between images are multiples of \( \frac{2L}{3} \), the distance between any two images cannot be \( \frac{3L}{2} \) (as this does not fit the form of \( \frac{2nL}{3} \) for any integer \( n \)).

### Final Answer:
The distance between any two images cannot be \( \frac{3L}{2} \).