The angle of polarisation for any medium is `60^@`. What will be critical angle for this?

Options

A. (a) `sin^-1sqrt3`
B. (b) `tan^-1sqrt3`
C. (c) `cos^-1sqrt3`
D. (d) `sin^-1(1)/(sqrt3)`

Explanation

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

### Step-by-Step Solution:

1. **Understand the relationship between the angle of polarization and the refractive index**:
The angle of polarization (\(\theta_p\)) is related to the refractive index (\(\mu\)) of the medium by the formula:
\[ \tan(\theta_p) = \mu \]

2. **Substitute the given angle of polarization**:
Given that \(\theta_p = 60^\circ\), we can substitute this value into the formula:
\[ \tan(60^\circ) = \mu \]

3. **Calculate \(\tan(60^\circ)\)**:
The value of \(\tan(60^\circ)\) is \(\sqrt{3}\). Therefore, we have:
\[ \mu = \sqrt{3} \]

4. **Use the refractive index to find the critical angle**:
The critical angle (\(\theta_c\)) can be calculated using the formula:
\[ \sin(\theta_c) = \frac{1}{\mu} \]
Substituting \(\mu = \sqrt{3}\):
\[ \sin(\theta_c) = \frac{1}{\sqrt{3}} \]

5. **Calculate the critical angle**:
To find \(\theta_c\), we take the inverse sine:
\[ \theta_c = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]

6. **Final result**:
The critical angle for the medium is:
\[ \theta_c = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]