If an object is placed between two plane mirrors a distance 2b, apart, the object is situated at mid point between mirrors, the position of nth image formed by the one of the mirrors with respect to the object is

Options

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

Explanation

To solve the problem of finding the position of the nth image formed by one of the plane mirrors with respect to the object, we can follow these steps:

### Step 1: Understand the setup
We have two plane mirrors facing each other, and an object is placed at the midpoint between them. The distance between the two mirrors is given as \(2b\). Therefore, the distance from the object to each mirror is \(b\).

### Step 2: Determine the position of the first image
The first image (\(I_1\)) is formed by the first mirror. Since the object is \(b\) away from this mirror, the distance of the first image from the object is:
\[ d_1 = b + b = 2b \]

### Step 3: Determine the position of the second image
The second image (\(I_2\)) is formed by the second mirror. The first image acts as an object for the second mirror. The distance of the first image from the second mirror is also \(b\), so the distance of the second image from the object is:
\[ d_2 = 2b + b = 3b \]

### Step 4: Determine the position of the third image
The third image (\(I_3\)) is formed by the first mirror again. The second image acts as an object for the first mirror. The distance of the second image from the first mirror is \(3b\), so the distance of the third image from the object is:
\[ d_3 = 3b + b = 4b \]

### Step 5: Identify the pattern
From the above calculations, we can observe a pattern in the distances:
- \(d_1 = 2b\)
- \(d_2 = 3b\)
- \(d_3 = 4b\)

Continuing this pattern, we can see that the distance of the nth image from the object can be expressed as:
\[ d_n = (n + 1)b \]

### Step 6: Generalize the formula
From the pattern, we can generalize that the distance of the nth image formed by one of the mirrors with respect to the object is:
\[ d_n = (n + 1)b \]

### Final Answer
Thus, the position of the nth image formed by one of the mirrors with respect to the object is:
\[ d_n = (n + 1)b \]

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