Two plane mirrors are inclined at some angle `theta`. If a ball is placed between the mirrors and there are 9 images formed for the ball, then angle `theta` may be equal to

Options

A. `45^@`
B. `60^@`
C. `36^@`
D. `90^@`

Explanation

To solve the problem of finding the angle \( \theta \) at which two plane mirrors form 9 images of a ball placed between them, we can use the formula for the number of images formed by two mirrors inclined at an angle \( \theta \):

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

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

### Step-by-step Solution:

1. **Identify the Number of Images**: We know from the problem that the number of images \( N \) is 9.

2. **Set Up the Equation**: Substitute \( N = 9 \) into the formula:
\[ 9 = \frac{360^\circ}{\theta} - 1 \]

3. **Rearrange the Equation**: Add 1 to both sides to isolate the fraction:
\[ 10 = \frac{360^\circ}{\theta} \]

4. **Cross-Multiply**: Multiply both sides by \( \theta \) to eliminate the fraction:
\[ 10\theta = 360^\circ \]

5. **Solve for \( \theta \)**: Divide both sides by 10:
\[ \theta = \frac{360^\circ}{10} = 36^\circ \]

### Conclusion:
The angle \( \theta \) at which the two mirrors are inclined to form 9 images of the ball is \( 36^\circ \).