The total number of images formed by two plane mirrors , inclined at an angle of `15^@` and an objectvitying symmetrically is

Options

A. 24
B. 23
C. 22
D. 25

Answer

To solve the problem of finding the total number of images formed by two plane mirrors inclined at an angle of \(15^\circ\) with an object placed symmetrically between them, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angle of Inclination**:
We have two plane mirrors inclined at an angle \(\theta = 15^\circ\).

2. **Calculate the Value of \( \frac{360^\circ}{\theta} \)**:
We need to determine how many times the angle of inclination fits into \(360^\circ\):
\[ \frac{360^\circ}{\theta} = \frac{360^\circ}{15^\circ} = 24 \]

3. **Determine if the Result is Even or Odd**:
The result \(24\) is an even number.

4. **Use the Formula for Number of Images**:
For two mirrors inclined at an angle \(\theta\) and when the object is placed symmetrically, the formula for the number of images \(n\) is given by:
\[ n = \frac{360^\circ}{\theta} - 1 \]
Since we found that \(\frac{360^\circ}{\theta} = 24\), we can substitute this value into the formula:
\[ n = 24 - 1 = 23 \]

5. **Conclusion**:
The total number of images formed by the two plane mirrors inclined at an angle of \(15^\circ\) is \(23\).

### Final Answer:
The total number of images formed is **23**.