The angle of polarisation for any medium is `60^(@)` , what will be critical angle for this

Options

A. `sin^(-1)sqrt(3)`
B. `tan^(-1)sqrt(3)`
C. `cos^(-1)sqrt(3)`
D. `sin^(-1)1/sqrt(3)`

Explanation

To find the critical angle when the angle of polarization for a medium is given as \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Angle of polarization, \( I_p = 60^\circ \).

2. **Use Brewster's Law:**
- According to Brewster's Law, the refractive index \( \mu \) of the medium can be calculated using the formula:
\[ \mu = \tan(I_p) \]
- Substituting the value of \( I_p \):
\[ \mu = \tan(60^\circ) \]

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

4. **Relate Refractive Index to Critical Angle:**
- The critical angle \( C \) can be found using the relationship:
\[ C = \sin^{-1}\left(\frac{1}{\mu}\right) \]

5. **Substitute the Value of Refractive Index:**
- Now, substituting \( \mu = \sqrt{3} \) into the formula for critical angle:
\[ C = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]

6. **Final Result:**
- Thus, the critical angle is:
\[ C = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]