A point object is placed midway between two plane mirrors a distance apart. The plane mirrors form an infinite number of images due to multiple reflections. The distance between `n^(th)` order images formed in the two mirrors is

Options

A. `na`
B. `2na`
C. `0.5na`
D. `n^2a`

Explanation

To find the distance between the `n^(th)` order images formed by two plane mirrors placed a distance `A` apart, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors facing each other with a distance `A` between them.
- A point object is placed at the midpoint between the two mirrors.

2. **Position of the Object**:
- The distance from the object to each mirror is `A/2`.

3. **Finding the First Order Images**:
- The first image (I1) is formed by the reflection of the object in the first mirror, and its distance from the object is `A/2`.
- The second image (I1') is formed by the reflection of the object in the second mirror, also at a distance of `A/2`.
- Therefore, the distance between I1 and I1' is:
\[ \text{Distance between I1 and I1'} = A/2 + A/2 = A \]

4. **Finding the Second Order Images**:
- The second order images (I2 and I2') are formed by the reflections of I1 and I1' in the opposite mirrors.
- The distance from the object to I2 is `A + A/2 = 3A/2`.
- Similarly, the distance from the object to I2' is also `3A/2`.
- Therefore, the distance between I2 and I2' is:
\[ \text{Distance between I2 and I2'} = 3A/2 + 3A/2 = 3A \]

5. **Finding the General Formula**:
- Continuing this pattern, we can see that the distance between the `n^(th)` order images (In and In') can be expressed as:
\[ \text{Distance between In and In'} = nA \]
- This is because each successive pair of images is separated by an additional `A` distance.

6. **Conclusion**:
- The distance between the `n^(th)` order images formed by the two mirrors is:
\[ \text{Distance} = nA \]

### Final Answer:
The distance between the `n^(th)` order images formed in the two mirrors is \( nA \).

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