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. `3xx10^(8)`
B. `(3/sqrt(2))xx10^(8)`
C. `sqrt(3)xx10^(8)`
D. `0.5xx10^(8)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the concept of polarization
When light reflects off a surface, it can become polarized. The angle of incidence at which the reflected light is completely polarized is known as the angle of polarization (Ip).

### Step 2: Identify the angle of incidence
According to the problem, the angle of incidence (Ip) is given as \(60^\circ\).

### Step 3: Use Brewster's Law
Brewster's Law states that the refractive index (μ) of a material is equal to the tangent of the angle of polarization:
\[ \mu = \tan(I_p) \]
Substituting \(I_p = 60^\circ\):
\[ \mu = \tan(60^\circ) \]

### Step 4: Calculate the refractive index
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Thus, the refractive index of the material is:
\[ \mu = \sqrt{3} \]

### Step 5: Relate the refractive index to the speed of light
The refractive index is also defined as:
\[ \mu = \frac{c}{v} \]
where \(c\) is the speed of light in vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)) and \(v\) is the speed of light in the material.

### Step 6: Rearrange to find the speed of light in the material
From the equation, we can rearrange to find \(v\):
\[ v = \frac{c}{\mu} \]
Substituting the values we have:
\[ v = \frac{3 \times 10^8}{\sqrt{3}} \]

### Step 7: Simplify the expression
To simplify:
\[ v = \frac{3 \times 10^8}{\sqrt{3}} = \frac{3\sqrt{3}}{3} \times 10^8 = \sqrt{3} \times 10^8 \, \text{m/s} \]

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

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