What should be the angle between two plane mirrorrs so that whatever be the angle of incidence, the incident ray and the reflected ray from the two mirrorrs be parallel to each other

Options

A. `60^(@)`
B. `90^(@)`
C. `120^(@)`
D. `45^(@)`

Explanation

To find the angle between two plane mirrors such that the incident ray and the reflected ray are parallel to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to determine the angle \( \theta \) between two plane mirrors such that the incident ray and the reflected ray are parallel.

2. **Deviation Concept**: When light reflects off mirrors, the total deviation \( \delta \) of the light ray can be calculated. For the incident ray and the reflected ray to be parallel, the total deviation must be \( 180^\circ \).

3. **Using the Deviation Formula**: The formula for the deviation \( \delta \) when light reflects off two mirrors is given by:
\[ \delta = 360^\circ - 2\theta \]
where \( \theta \) is the angle between the two mirrors.

4. **Setting Up the Equation**: Since we established that \( \delta = 180^\circ \), we can set up the equation:
\[ 180^\circ = 360^\circ - 2\theta \]

5. **Solving for \( \theta \)**:
- Rearranging the equation gives:
\[ 2\theta = 360^\circ - 180^\circ \]
- Simplifying this results in:
\[ 2\theta = 180^\circ \]
- Dividing both sides by 2 yields:
\[ \theta = \frac{180^\circ}{2} = 90^\circ \]

6. **Conclusion**: The angle \( \theta \) between the two plane mirrors should be \( 90^\circ \).

### Final Answer:
The angle between the two plane mirrors should be \( 90^\circ \).

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