If the polarising angle for a medium is `45^@`, what is the refractive index of that medium?

Options

A. 1
B. 1.3
C. 1.5
D. 0.9

Answer

To find the refractive index of a medium given that the polarizing angle is \( 45^\circ \), we can use Brewster's Law. Brewster's Law states that the tangent of the polarizing angle (\( \theta_P \)) is equal to the refractive index (\( \mu \)) of the medium when light is incident from air.

### Step-by-Step Solution:

1. **Identify the given polarizing angle**:
The polarizing angle \( \theta_P \) is given as \( 45^\circ \).

2. **Apply Brewster's Law**:
Brewster's Law states that:
\[ \tan(\theta_P) = \mu \]
where \( \mu \) is the refractive index of the medium.

3. **Calculate the tangent of the polarizing angle**:
Since \( \theta_P = 45^\circ \):
\[ \tan(45^\circ) = 1 \]

4. **Substitute the value into Brewster's Law**:
\[ \mu = \tan(45^\circ) = 1 \]

5. **Conclusion**:
The refractive index of the medium is \( \mu = 1 \).

### Final Answer:
The refractive index of the medium is \( 1 \).