The angle of incidence of a light beam onto a reflecting surface is continuously varied. The reflected ray is found to be completely polarized when the angle of incidence is `60^(@)`. What is the index of refraction of the reflecting material ?

Options

A. `(sqrt3)/(2)`
B. `(2)/(sqrt3)`
C. `sqrt3`
D. `2`

Explanation

To find the index of refraction of the reflecting material when the angle of incidence is 60 degrees and complete polarization occurs, we can use Brewster's Law.

### Step-by-Step Solution:

1. **Understanding Brewster's Angle**:
Brewster's angle (θ_B) is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. At this angle, the reflected and refracted rays are perpendicular to each other.

2. **Using the Formula for Brewster's Angle**:
The formula for Brewster's angle is given by:
\[ \tan(\theta_B) = \frac{n_2}{n_1} \]
where \( n_1 \) is the index of refraction of the first medium (air, in this case, which is approximately 1), and \( n_2 \) is the index of refraction of the second medium (the reflecting material).

3. **Identifying the Given Angle**:
From the problem, we know that the angle of incidence (θ_B) is 60 degrees.

4. **Calculating the Index of Refraction**:
Using the Brewster's angle formula:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore, we can set up the equation:
\[ \sqrt{3} = \frac{n_2}{1} \]
This simplifies to:
\[ n_2 = \sqrt{3} \]

5. **Conclusion**:
The index of refraction of the reflecting material is:
\[ n_2 \approx 1.732 \]

### Final Answer:
The index of refraction of the reflecting material is approximately **1.732**.