When the angle of incidence is `60^(@)` on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is

Options

A. `sqrt(2)xx10^(8)ms^(-1)`
B. `sqrt(3)xx10^(8)ms^(-1)`
C. `2xx10^(8)ms^(-1)`
D. `3xx10^(8)ms^(-1)`

Explanation

To solve the problem, we need to find the velocity of light in glass when the angle of incidence is given as \(60^\circ\) and the reflected ray is completely polarized.

### Step-by-Step Solution:

1. **Understanding Polarization Condition**:
When light is completely polarized upon reflection, the angle of incidence (\(i\)) is equal to Brewster's angle (\(\theta_B\)). The relationship between the refractive index (\(\mu\)) of the medium and Brewster's angle is given by:
\[ \mu = \tan(\theta_B) \]
Since the angle of incidence is \(60^\circ\), we can say:
\[ \theta_B = 60^\circ \]

2. **Calculating the Refractive Index**:
We can calculate the refractive index of glass using the tangent of the Brewster's angle:
\[ \mu = \tan(60^\circ) \]
We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore:
\[ \mu = \sqrt{3} \]

3. **Finding the Velocity of Light in Glass**:
The speed of light in a medium is related to the speed of light in vacuum (\(c\)) and the refractive index (\(\mu\)) by the formula:
\[ v = \frac{c}{\mu} \]
The speed of light in vacuum is:
\[ c = 3 \times 10^8 \, \text{m/s} \]
Substituting the values we have:
\[ v = \frac{3 \times 10^8}{\sqrt{3}} \, \text{m/s} \]

4. **Calculating the Final Velocity**:
To simplify, we can express the velocity of light in glass as:
\[ v = \frac{3 \times 10^8}{\sqrt{3}} \approx 1.732 \times 10^8 \, \text{m/s} \]
Thus, the velocity of light in glass is:
\[ v \approx \sqrt{3} \times 10^8 \, \text{m/s} \]

### Final Answer:
The velocity of light in glass is approximately \(1.732 \times 10^8 \, \text{m/s}\).