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

Options

A. (a)5
B. (b)9
C. (c)7
D. (d)8

Answer

To determine the number of images formed when an object is placed between two plane mirrors that are at an angle of \(45^\circ\) to each other, we can use the formula for calculating the number of images formed by two mirrors:

### Step-by-Step Solution:

1. **Identify the Angle Between the Mirrors**:
The angle (\(\phi\)) between the two plane mirrors is given as \(45^\circ\).

2. **Use the Formula for Number of Images**:
The formula to calculate the number of images (\(N\)) formed by two plane mirrors is:
\[ N = \frac{360^\circ}{\phi} - 1 \]
where \(\phi\) is the angle between the mirrors.

3. **Substitute the Angle into the Formula**:
Substitute \(\phi = 45^\circ\) into the formula:
\[ N = \frac{360^\circ}{45^\circ} - 1 \]

4. **Calculate the Value**:
Calculate \(\frac{360}{45}\):
\[ \frac{360}{45} = 8 \]
Therefore,
\[ N = 8 - 1 = 7 \]

5. **Conclusion**:
The total number of images formed when an object is placed between two plane mirrors at \(45^\circ\) to each other is \(7\).

### Final Answer:
The number of images formed is **7**.

---