Assertion : Two plane mirrors kept at right angles deviate any ray of light by `180^@` after two reflection.
Reason : The above condition is satisfied only for angle of incidence `i=45^@`.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Answer

To solve the given question, we need to analyze the assertion and the reason provided.

**Assertion:** Two plane mirrors kept at right angles deviate any ray of light by \(180^\circ\) after two reflections.

**Reason:** The above condition is satisfied only for angle of incidence \(i = 45^\circ\).

### Step-by-Step Solution:

1. **Understanding the Setup:**
- We have two plane mirrors placed at a right angle (90 degrees) to each other.
- When a ray of light strikes the first mirror, it reflects according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

2. **First Reflection:**
- Let’s denote the angle of incidence on the first mirror as \(i\).
- After the first reflection, the ray will reflect off the first mirror and travel towards the second mirror.

3. **Second Reflection:**
- Upon reaching the second mirror, the angle of incidence will be \(90^\circ - i\) (since the mirrors are at right angles).
- The angle of reflection from the second mirror will also be \(90^\circ - i\).

4. **Calculating the Total Deviation:**
- The total deviation of the ray after two reflections can be calculated as follows:
- The first reflection changes the direction of the ray by \(2i\) (since the angle of incidence equals the angle of reflection).
- The second reflection also changes the direction by \(2(90^\circ - i)\).
- Therefore, the total deviation is:
\[ \text{Total Deviation} = 2i + 2(90^\circ - i) = 180^\circ \]
- This shows that the ray is deviated by \(180^\circ\) regardless of the angle of incidence \(i\).

5. **Evaluating the Reason:**
- The reason states that this condition is satisfied only for \(i = 45^\circ\). However, as shown, the total deviation of \(180^\circ\) occurs for any angle of incidence \(i\).
- Therefore, the reason is false.

6. **Conclusion:**
- The assertion is true because two plane mirrors at right angles do indeed deviate light by \(180^\circ\) after two reflections.
- The reason is false because this condition is not limited to \(i = 45^\circ\).

### Final Answer:
- **Assertion:** True
- **Reason:** False