To get three images of a single object, one should have two plane mirrors at an angle of

Options

A. `60^circ`
B. `90^circ`
C. `120^circ`
D. `30^circ`

Explanation

To determine the angle at which two plane mirrors should be placed to create three images of a single object, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Formula**:
The number of images (N) formed by two mirrors placed at an angle θ can be calculated using the formula:
\[ N = \frac{360}{\theta} - 1 \]
Here, N is the number of images, and θ is the angle between the two mirrors.

2. **Setting Up the Equation**:
We want to find the angle θ such that the number of images N equals 3. Therefore, we set up the equation:
\[ 3 = \frac{360}{\theta} - 1 \]

3. **Rearranging the Equation**:
To isolate θ, we first add 1 to both sides:
\[ 3 + 1 = \frac{360}{\theta} \]
This simplifies to:
\[ 4 = \frac{360}{\theta} \]

4. **Cross-Multiplying**:
We can cross-multiply to solve for θ:
\[ 4\theta = 360 \]

5. **Dividing to Find θ**:
Now, divide both sides by 4:
\[ \theta = \frac{360}{4} = 90 \text{ degrees} \]

6. **Conclusion**:
Therefore, to get three images of a single object, the two plane mirrors should be placed at an angle of 90 degrees.

### Final Answer:
The angle between the two plane mirrors should be **90 degrees**.

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