Two plane mirrors are at `45^(@)` to each other. If an object is placed between them, then the number of images will be

Options

A. 5
B. 9
C. 7
D. 8

Answer

To find the number of images formed by two plane mirrors placed at an angle of \(45^\circ\) to each other, we can use the formula for the number of images created 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 \(\theta = 45^\circ\).

2. **Substitute the angle into the formula**:
We substitute \(\theta\) into the formula:
\[ N = \frac{360^\circ}{45^\circ} - 1 \]

3. **Calculate \(\frac{360^\circ}{45^\circ}\)**:
\[ \frac{360}{45} = 8 \]

4. **Subtract 1 from the result**:
\[ N = 8 - 1 = 7 \]

5. **Conclusion**:
The total number of images formed is \(7\).

### Final Answer:
The number of images formed by two plane mirrors at \(45^\circ\) to each other is **7**.

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