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, we can use the formula for the number of images formed by two mirrors:

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

where \(N\) is the number of images and \(\theta\) is the angle between the two mirrors.

### Step-by-Step Solution:

1. **Identify the angle between the mirrors**:
Given that the angle \(\theta = 112.5^\circ\).

2. **Use the formula to calculate the number of images**:
Substitute \(\theta\) into the formula:
\[ N = \frac{360^\circ}{112.5^\circ} - 1 \]

3. **Calculate \(\frac{360^\circ}{112.5^\circ}\)**:
\[ \frac{360}{112.5} = 3.2 \]

4. **Subtract 1 from the result**:
\[ N = 3.2 - 1 = 2.2 \]

5. **Interpret the result**:
Since the number of images must be a whole number, we round \(2.2\) to the nearest whole number, which is \(2\).

### Final Answer:
The total number of images formed by the two plane mirrors inclined at an angle of \(112.5^\circ\) is **2**.