An object is placed between two plane mirrors inclined at an angle to each other. If the number of images formed is 7 then the angle of inclination is -

Options

A. ` 15^(@)`
B. ` 30^(@)`
C. ` 45^(@)`
D. ` 90^(@)`

Answer

To find the angle of inclination between two plane mirrors that form a specific number of images, we can use the formula for the number of images formed by two mirrors inclined at an angle \( \theta \):

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

Where \( N \) is the number of images formed.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The number of images \( N = 7 \).

2. **Set Up the Equation:**
- Substitute \( N \) into the formula:
\[ 7 = \frac{360}{\theta} - 1 \]

3. **Rearrange the Equation:**
- Add 1 to both sides:
\[ 7 + 1 = \frac{360}{\theta} \]
\[ 8 = \frac{360}{\theta} \]

4. **Solve for \( \theta \):**
- Rearranging gives:
\[ \theta = \frac{360}{8} \]
- Calculate \( \theta \):
\[ \theta = 45 \text{ degrees} \]

5. **Conclusion:**
- The angle of inclination between the two mirrors is \( 45 \) degrees.

### Final Answer:
The angle of inclination is \( 45 \) degrees.