If the refractive index of glass is ` sqrt(3)`, then its polarising angle will be

Options

A. `30^(@)`
B. `45^(@) `
C. `60^(@)`
D. `90^(@)`

Explanation

To find the polarizing angle (IP) for glass with a refractive index of \( \sqrt{3} \), we can use Brewster's Law, which states:

\[ \tan(\theta_P) = \frac{n_2}{n_1} \]

Where:
- \( \theta_P \) is the polarizing angle,
- \( n_1 \) is the refractive index of the first medium (air in this case, which is approximately 1),
- \( n_2 \) is the refractive index of the second medium (glass in this case, given as \( \sqrt{3} \)).

### Step-by-Step Solution:

1. **Identify the Refractive Indices:**
- For air, \( n_1 = 1 \).
- For glass, \( n_2 = \sqrt{3} \).

2. **Apply Brewster's Law:**
\[ \tan(\theta_P) = \frac{n_2}{n_1} = \frac{\sqrt{3}}{1} = \sqrt{3} \]

3. **Find the Polarizing Angle:**
- To find \( \theta_P \), we need to take the arctangent (inverse tangent) of \( \sqrt{3} \):
\[ \theta_P = \tan^{-1}(\sqrt{3}) \]

4. **Calculate the Angle:**
- The value of \( \tan^{-1}(\sqrt{3}) \) corresponds to \( 60^\circ \) because:
\[ \tan(60^\circ) = \sqrt{3} \]

5. **Conclusion:**
- Therefore, the polarizing angle \( \theta_P \) is:
\[ \theta_P = 60^\circ \]

### Final Answer:
The polarizing angle for glass with a refractive index of \( \sqrt{3} \) is \( 60^\circ \).

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