For a diven medium, the polarising angle is `60^(@)`. What will be the critical angle for this medium ?

Answer

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

### Step-by-Step Solution:

1. **Understanding Polarizing Angle**: The polarizing angle (\(I_p\)) is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. According to Brewster's Law, the polarizing angle is related to the refractive index (\(n\)) of the medium.

2. **Using Brewster's Law**: Brewster's Law states that:
\[ \tan(I_p) = n \]
Given that \(I_p = 60^\circ\), we can find the refractive index:
\[ n = \tan(60^\circ) \]

3. **Calculating the Refractive Index**: We know that:
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore, the refractive index \(n\) of the medium is:
\[ n = \sqrt{3} \]

4. **Finding the Critical Angle**: The critical angle (\(I_c\)) can be calculated using the formula:
\[ I_c = \sin^{-1}\left(\frac{1}{n}\right) \]
Substituting the value of \(n\):
\[ I_c = \sin^{-1}\left(\frac{1}{\sqrt{3}}\right) \]

5. **Calculating the Critical Angle**: We know that:
\[ \frac{1}{\sqrt{3}} \approx 0.577 \]
Using a calculator or trigonometric tables, we find:
\[ I_c \approx 35.26^\circ \]

6. **Conclusion**: Therefore, the critical angle for the medium is:
\[ I_c \approx 35.26^\circ \]

### Final Answer:
The critical angle for the medium is approximately \(35.26^\circ\).

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