When the angle of incidence on a material is `60^(@)`, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in `ms^(-1)`)

Options

A. `3 xx 10^(4)`
B. `3/sqrt(2) xx 10^(8)`
C. `sqrt(3) xx 10^(8)`
D. `0.5 xx 10^(8)`

Answer

To solve the problem, we need to determine the velocity of the refracted ray inside the material when the angle of incidence is \(60^\circ\) and the reflected light is completely polarized. This situation indicates that we can use Brewster's Law.

### Step-by-Step Solution:

1. **Understanding Brewster's Law**: Brewster's Law states that the angle of incidence (\(i_B\)) at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection, is given by:
\[ \tan(i_B) = \frac{n_2}{n_1} \]
where \(n_1\) is the refractive index of the first medium (usually air, \(n_1 \approx 1\)) and \(n_2\) is the refractive index of the second medium.

2. **Identifying the Angle of Incidence**: In this case, we are given that the angle of incidence is \(60^\circ\). According to Brewster's Law, this angle is the angle of polarization, which means:
\[ \tan(60^\circ) = \sqrt{3} \]

3. **Calculating the Refractive Index**: Using Brewster's Law, we can find the refractive index of the material:
\[ \tan(60^\circ) = \frac{n_2}{n_1} \implies \sqrt{3} = n_2 \implies n_2 = \sqrt{3} \]

4. **Using the Formula for Velocity**: The velocity of light in a medium is given by the equation:
\[ V = \frac{C}{n} \]
where \(C\) is the speed of light in vacuum (\(C \approx 3 \times 10^8 \, \text{m/s}\)) and \(n\) is the refractive index of the medium.

5. **Substituting the Values**: Now, substituting the values into the formula:
\[ V = \frac{C}{\sqrt{3}} = \frac{3 \times 10^8}{\sqrt{3}} \, \text{m/s} \]

6. **Calculating the Result**: To simplify this, we can express it as:
\[ V = \frac{3 \times 10^8}{\sqrt{3}} = \sqrt{3} \times 10^8 \, \text{m/s} \]

### Final Answer:
The velocity of the refracted ray inside the material is:
\[ V = \sqrt{3} \times 10^8 \, \text{m/s} \]