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

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `150^(@)`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We are given that the number of images (n) is 3.

2. **Use the Formula for the Number of Images:**
- The formula for the number of images formed by two plane mirrors is given by:
\[ n = \frac{360^\circ}{\theta} - 1 \]
- Here, \( \theta \) is the angle between the two mirrors.

3. **Substitute the Given Value into the Formula:**
- We know \( n = 3 \). Therefore, we can substitute this value into the formula:
\[ 3 = \frac{360^\circ}{\theta} - 1 \]

4. **Rearrange the Equation:**
- To isolate \( \theta \), first add 1 to both sides:
\[ 3 + 1 = \frac{360^\circ}{\theta} \]
\[ 4 = \frac{360^\circ}{\theta} \]

5. **Solve for \( \theta \):**
- Now, we can rearrange the equation to solve for \( \theta \):
\[ \theta = \frac{360^\circ}{4} \]

6. **Calculate the Value of \( \theta \):**
- Performing the division:
\[ \theta = 90^\circ \]

7. **Conclusion:**
- Therefore, the angle between the two plane mirrors should be \( 90^\circ \) to obtain three images of a single object.

### Final Answer:
The angle at which the two plane mirrors should be placed is \( 90^\circ \).

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