If two mirrors are inclined at some angle `theta`. An object is placed between the mirrors and there are 5 images formed for an object, then `theta` is may be

Options

A. `45^(@)`
B. `53^(@)`
C. `63^(@)`
D. `75^(@)`

Answer

To solve the problem of finding the angle \( \theta \) between two mirrors that form 5 images of an object placed between them, we can use the formula for the number of images formed by two inclined mirrors.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The number of images \( n \) formed by two mirrors inclined at an angle \( \theta \) is given by the formula:
\[ n = \frac{360}{\theta} - 1 \]
This formula applies when the object is placed symmetrically between the mirrors.

2. **Setting Up the Equation**:
Given that there are 5 images formed, we can set up the equation:
\[ 5 = \frac{360}{\theta} - 1 \]

3. **Rearranging the Equation**:
To isolate \( \theta \), we first add 1 to both sides:
\[ 6 = \frac{360}{\theta} \]

4. **Cross-Multiplying**:
Now, we can cross-multiply to solve for \( \theta \):
\[ 6\theta = 360 \]

5. **Dividing to Find \( \theta \)**:
Divide both sides by 6:
\[ \theta = \frac{360}{6} = 60 \text{ degrees} \]

6. **Conclusion**:
Therefore, the angle \( \theta \) between the two mirrors is \( 60 \) degrees.

### Final Answer:
The angle \( \theta \) may be \( 60 \) degrees.