A ray of light is incident at `50^(@)` on the middle of one of the two mirrors arranged at an angle of `60^(@)` between them . The ray then touches the second mirror, get reflected back to the first mirror, making an angle of incidence of

Options

A. `50^(@)`
B. `60^(@)`
C. `70^(@)`
D. `80^(@)`

Explanation

To solve the problem, we need to analyze the geometry of the two mirrors and the angles involved when the ray of light reflects off them.

### Step-by-Step Solution:

1. **Identify the Angles**:
- We have two mirrors arranged at an angle of \(60^\circ\) to each other.
- A ray of light is incident on the first mirror at an angle of \(50^\circ\) to the normal.

2. **Determine the Angle of Reflection**:
- According to the law of reflection, the angle of incidence is equal to the angle of reflection.
- Therefore, the angle of reflection from the first mirror is also \(50^\circ\).

3. **Calculate the Angle Between the Reflected Ray and the Second Mirror**:
- The angle between the two mirrors is \(60^\circ\).
- The angle of reflection from the first mirror is \(50^\circ\), which means the angle between the reflected ray and the normal to the second mirror can be calculated as follows:
- The angle between the reflected ray and the second mirror is \(60^\circ - 50^\circ = 10^\circ\).

4. **Determine the Angle of Incidence on the Second Mirror**:
- The angle of incidence on the second mirror is equal to the angle between the reflected ray and the normal to the second mirror.
- Therefore, the angle of incidence on the second mirror is \(10^\circ\).

5. **Calculate the Angle of Reflection from the Second Mirror**:
- Again, using the law of reflection, the angle of incidence on the second mirror is equal to the angle of reflection.
- Thus, the angle of reflection from the second mirror is also \(10^\circ\).

6. **Final Calculation**:
- The ray then reflects back towards the first mirror. The angle of incidence when it strikes the first mirror again will be equal to the angle of reflection from the second mirror, which is \(10^\circ\).

### Conclusion:
The angle of incidence of the ray when it reflects back to the first mirror is \(10^\circ\).

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