Two plane mirros are inclined at an anle `theta`. It is found that a ray incident on one mirror at any angle is rendered paralle ot itself after reflection from both the mirrors. The value of `theta` is

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `120^(@)`

Explanation

To solve the problem, we need to determine the angle \( \theta \) between two plane mirrors such that a ray incident on one mirror at any angle is rendered parallel to itself after reflection from both mirrors.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two plane mirrors inclined at an angle \( \theta \).
- A ray of light strikes one of the mirrors and after reflecting from both mirrors, it emerges parallel to its original direction.

2. **Concept of Deviation**:
- When a ray of light reflects off a mirror, it undergoes a deviation. For two mirrors inclined at an angle \( \theta \), the total deviation \( \delta \) of the ray after reflecting off both mirrors is given by:
\[ \delta = 2\theta \]
- This means that the ray is effectively rotated by an angle of \( 2\theta \).

3. **Condition for Parallelism**:
- For the ray to emerge parallel to its original direction, the total deviation must be equal to \( 180^\circ \) (i.e., the ray is turned halfway around).
- Therefore, we set up the equation:
\[ 2\theta = 180^\circ \]

4. **Solving for \( \theta \)**:
- Dividing both sides of the equation by 2 gives:
\[ \theta = \frac{180^\circ}{2} = 90^\circ \]

5. **Conclusion**:
- The angle \( \theta \) between the two mirrors must be \( 90^\circ \) for the ray to emerge parallel to itself after reflection.

### Final Answer:
The value of \( \theta \) is \( 90^\circ \).

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