Two plane mirrors are placed parallel to each other at a distance L apart . A point object O is 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/2
C. 2L
D. None of these

Explanation

To solve the problem of determining the distance between any two images formed by two parallel mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors 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 one mirror (let's call it Mirror 1).

2. **Calculating Distances**:
- The distance from the object \( O \) to Mirror 1 is \( \frac{L}{3} \).
- The distance from \( O \) to Mirror 2 is \( L - \frac{L}{3} = \frac{2L}{3} \).

3. **Finding the First Set of Images**:
- The first image \( I_1 \) formed by Mirror 1 will be at a distance \( \frac{L}{3} \) behind Mirror 1. Therefore, the position of \( I_1 \) is:
\[ I_1 = -\frac{L}{3} \]
- The first image \( I_2 \) formed by Mirror 2 will be at a distance \( \frac{2L}{3} \) behind Mirror 2. Therefore, the position of \( I_2 \) is:
\[ I_2 = L + \frac{2L}{3} = \frac{5L}{3} \]

4. **Finding Subsequent Images**:
- The image \( I_1 \) acts as an object for Mirror 2, and it will form another image \( I_2' \) at a distance \( L + \frac{L}{3} = \frac{4L}{3} \) from Mirror 2.
- The image \( I_2 \) acts as an object for Mirror 1, forming another image \( I_1' \) at a distance \( L + \frac{2L}{3} = \frac{5L}{3} \) from Mirror 1.

5. **Generalizing the Image Positions**:
- The positions of the images can be generalized. The \( n \)-th image from Mirror 1 can be represented as:
\[ I_{n} = (-1)^{n+1} \left( nL + \frac{L}{3} \right) \]
- The \( n \)-th image from Mirror 2 can be represented as:
\[ I_{n} = (-1)^{n} \left( nL + \frac{2L}{3} \right) \]

6. **Calculating Distances Between Images**:
- The distance between two consecutive images can be calculated. For example, the distance between \( I_1 \) and \( I_2 \) is:
\[ d = \left| I_2 - I_1 \right| = \left| \frac{5L}{3} - \left(-\frac{L}{3}\right) \right| = \frac{6L}{3} = 2L \]
- Similarly, the distance between any two images can be generalized as \( d = L \) or \( d = 2L \).

7. **Conclusion**:
- The distance between any two images cannot be \( \frac{3L}{2} \), as it does not fit into the pattern of distances derived from the image positions.

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