A beam of light is partially reflected and partially refracted from a surface. The angle between reflected and refracted light ray is `90^(@)`. If the angle of refraction is `30^(@)`, the angle of incidence is

Options

A. `60^(@)`
B. `48^(@)`
C. `45^(@)`
D. `90^(@)`

Answer

To find the angle of incidence when a beam of light is partially reflected and partially refracted, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The angle between the reflected ray and the refracted ray is \(90^\circ\).
- The angle of refraction (\(r\)) is \(30^\circ\).

2. **Draw a Diagram**:
- Draw a surface where the light beam strikes.
- Mark the angle of incidence (\(i\)), the angle of reflection (\(r\)), and the angle between the reflected and refracted rays.

3. **Use the Relationship Between Angles**:
- According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, if the angle of refraction is \(30^\circ\), we can denote the angle of reflection as \(r\).
- Since the angle between the reflected ray and the refracted ray is \(90^\circ\), we can write:
\[ i + r = 90^\circ \]
- Given that \(r = 30^\circ\), we can substitute this value into the equation:
\[ i + 30^\circ = 90^\circ \]

4. **Solve for the Angle of Incidence**:
- Rearranging the equation gives:
\[ i = 90^\circ - 30^\circ \]
- Therefore:
\[ i = 60^\circ \]

5. **Conclusion**:
- The angle of incidence is \(60^\circ\).

### Final Answer:
The angle of incidence is \(60^\circ\).