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 image. The distance between any two images cannot be

Options

A. `(3L)/(2)`
B. `(2L)/(3)`
C. `2L`
D. `L`

Answer

To solve the problem, we will analyze the situation with two parallel mirrors and the multiple images formed by a point object placed between them.

### Step-by-Step Solution:

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

2. **Positioning the Object**:
- Let’s denote the position of the object O as \( O \).
- The distance from O to M1 is \( \frac{L}{3} \).
- Therefore, the distance from O to M2 is \( L - \frac{L}{3} = \frac{2L}{3} \).

3. **Finding the Images**:
- The first image \( O_1 \) formed by mirror M1 will be at a distance \( \frac{L}{3} \) from M1, which means it is located at the same distance on the opposite side of M1.
- The second image \( O_2 \) formed by mirror M2 will be at a distance \( \frac{2L}{3} \) from M2, which is the same as \( L - \frac{L}{3} = \frac{2L}{3} \) from M1.

4. **Calculating Distances Between Images**:
- The distance between the first image \( O_1 \) and the second image \( O_2 \) is:
\[ \text{Distance}(O_1, O_2) = \left(\frac{L}{3} + \frac{2L}{3}\right) = L \]

5. **Continuing to Find More Images**:
- The third image \( O_3 \) will be the reflection of \( O_1 \) in M2, which is located at:
\[ \text{Distance from M2} = \frac{L}{3} + L = \frac{4L}{3} \]
- The fourth image \( O_4 \) will be the reflection of \( O_2 \) in M1, which is located at:
\[ \text{Distance from M1} = \frac{2L}{3} + L = \frac{5L}{3} \]

6. **Calculating Distances Between Other Images**:
- The distance between \( O_3 \) and \( O_4 \) can be calculated as:
\[ \text{Distance}(O_3, O_4) = \left(\frac{5L}{3} - \frac{4L}{3}\right) = \frac{L}{3} \]

7. **Identifying Distances That Cannot Occur**:
- We have calculated the distances between various images:
- \( O_1 \) to \( O_2 \): \( L \)
- \( O_3 \) to \( O_4 \): \( \frac{L}{3} \)
- Other combinations yield distances of \( 2L \) and \( \frac{2L}{3} \).
- However, the distance \( \frac{3L}{2} \) does not appear in any of the calculations.

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