A beam of light strikes a surface at angle of incidence of `60^(@)` and reflected beam becomes completely polarised . The refractive index of glass surface is -

Options

A. 1.5
B. `sqrt3`
C. `sqrt2`
D. `3/2`

Answer

To solve the problem, we need to find the refractive index of the glass surface when a beam of light strikes it at an angle of incidence of \(60^\circ\) and the reflected beam becomes completely polarized.

### Step-by-Step Solution:

1. **Understand the condition for complete polarization**:
When light is reflected at a certain angle, it can become completely polarized. This occurs at Brewster's angle, which is given by the formula:
\[ \tan(\theta_B) = \mu \]
where \(\theta_B\) is Brewster's angle and \(\mu\) is the refractive index of the medium.

2. **Identify the angle of incidence**:
The angle of incidence \(i\) is given as \(60^\circ\). According to the problem, the reflected ray is completely polarized at this angle.

3. **Relate the angles**:
For complete polarization, the angle of incidence \(i\) is equal to Brewster's angle \(\theta_B\):
\[ i = \theta_B = 60^\circ \]

4. **Calculate the refractive index**:
Using the relationship for Brewster's angle:
\[ \tan(60^\circ) = \mu \]
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore, we can conclude:
\[ \mu = \sqrt{3} \]

5. **Final Answer**:
The refractive index of the glass surface is:
\[ \mu = \sqrt{3} \]