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^(8)`
B. `(3/(sqrt2)) 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.

### Step-by-step Solution:

1. **Understanding Brewster's Law**:
Brewster's law states that the angle of incidence at which light is completely polarized upon reflection is given by:
\[ \mu = \tan(I) \]
where \( \mu \) is the refractive index of the material and \( I \) is the angle of incidence.

2. **Given Values**:
- Angle of incidence, \( I = 60^\circ \)
- Speed of light in vacuum, \( C = 3 \times 10^8 \, \text{m/s} \)

3. **Calculate the Refractive Index**:
Using Brewster's law:
\[ \mu = \tan(60^\circ) \]
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore:
\[ \mu = \sqrt{3} \]

4. **Relating Refractive Index to Velocity**:
The refractive index \( \mu \) is also defined as:
\[ \mu = \frac{C}{V} \]
where \( V \) is the velocity of light in the material.

5. **Substituting Values**:
From the above equation, we can express \( V \):
\[ V = \frac{C}{\mu} \]
Substituting the values we have:
\[ V = \frac{3 \times 10^8}{\sqrt{3}} \]

6. **Calculating the Velocity**:
To simplify:
\[ V = 3 \times 10^8 \div \sqrt{3} \]
This can be further simplified as:
\[ V = \sqrt{3} \times 10^8 \, \text{m/s} \]

7. **Final Result**:
Thus, the velocity of the refracted ray inside the material is:
\[ V \approx 1.732 \times 10^8 \, \text{m/s} \]

### Answer:
The velocity of the refracted ray inside the material is approximately \( 1.732 \times 10^8 \, \text{m/s} \).