Two plane mirrors are placed at some angle. There are five images formed when an object is placed symmetrically between them . Find the angle between the mirrors.

Options

A. `60^@`
B. `45^@`
C. `30^@`
D. `90^@`

Answer

To solve the problem of finding the angle between two plane mirrors that form five images when an object is placed symmetrically between them, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the number of images and the angle**:
The formula to find the number of images (N) formed by two plane mirrors placed at an angle (θ) is given by:
\[ N = \frac{360^\circ}{\theta} - 1 \]

2. **Set up the equation with the given number of images**:
According to the problem, the number of images formed (N) is 5. Therefore, we can write:
\[ 5 = \frac{360^\circ}{\theta} - 1 \]

3. **Rearrange the equation**:
To isolate θ, we first add 1 to both sides:
\[ 5 + 1 = \frac{360^\circ}{\theta} \]
This simplifies to:
\[ 6 = \frac{360^\circ}{\theta} \]

4. **Solve for θ**:
Now, we can solve for θ by multiplying both sides by θ and then dividing by 6:
\[ \theta = \frac{360^\circ}{6} \]

5. **Calculate the angle**:
Performing the division gives:
\[ \theta = 60^\circ \]

6. **Conclusion**:
The angle between the two mirrors is \(60^\circ\).

### Final Answer:
The angle between the mirrors is \(60^\circ\).

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