The total number of image formed by two plane mirrors, inclined at an angle of `112.5^@` and an object lying symmetrically is

Options

A. 3
B. 4
C. 2
D. 3.2

Answer

To find the total number of images formed by two plane mirrors inclined at an angle of \(112.5^\circ\) with an object lying symmetrically between them, we can follow these steps:

### Step 1: Identify the angle between the mirrors
The angle \( \theta \) between the two mirrors is given as \(112.5^\circ\).

### Step 2: Calculate the number of images using the formula
The formula to calculate the number of images \(N\) formed by two plane mirrors inclined at an angle \( \theta \) is given by:

\[ N = \frac{360^\circ}{\theta} - 1 \]

### Step 3: Substitute the value of \( \theta \)
Substituting \( \theta = 112.5^\circ \) into the formula:

\[ N = \frac{360^\circ}{112.5^\circ} - 1 \]

### Step 4: Perform the division
Now, calculate \( \frac{360}{112.5} \):

\[ \frac{360}{112.5} = 3.2 \]

### Step 5: Determine if the result is odd or even
Since \(3.2\) is not an integer, we take the integer part, which is \(3\). This indicates that the number of images formed is odd.

### Step 6: Apply the adjusted formula for odd results
When the result is odd, we use the formula:

\[ N = \left(\frac{360}{\theta}\right) - 1 \]

Substituting the integer part:

\[ N = 3 - 1 = 2 \]

### Conclusion
Thus, the total number of images formed by the two plane mirrors inclined at an angle of \(112.5^\circ\) is \(2\).

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