Unpolarized light is incident on a plane glass surface having refractive index . The angle of incidence at which reflected and refracted rays would become perpendicular to each other is :

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To find the angle of incidence at which the reflected and refracted rays become perpendicular to each other, we can use the concept of the angle of polarization.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have unpolarized light incident on a plane glass surface with a refractive index (μ) of √3. We need to find the angle of incidence (i) at which the reflected and refracted rays are perpendicular to each other.

2. **Using the Condition for Perpendicular Rays**:
When the reflected and refracted rays are perpendicular, the angle of incidence (i) is equal to the angle of polarization (IP). Thus, we can write:
\[ i = IP \]

3. **Relating Refractive Index and Angle of Polarization**:
The angle of polarization (IP) is related to the refractive index (μ) by the formula:
\[ \mu = \tan(IP) \]
Given that μ = √3, we can substitute this into the equation:
\[ \sqrt{3} = \tan(IP) \]

4. **Finding the Angle of Polarization**:
To find IP, we take the arctangent (inverse tangent) of √3:
\[ IP = \tan^{-1}(\sqrt{3}) \]

5. **Calculating the Angle**:
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore:
\[ IP = 60^\circ \]

6. **Conclusion**:
Since the angle of incidence (i) is equal to the angle of polarization (IP), we have:
\[ i = 60^\circ \]
Thus, the angle of incidence at which the reflected and refracted rays become perpendicular is **60 degrees**.

### Final Answer:
The angle of incidence at which reflected and refracted rays become perpendicular is **60 degrees**.

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