The critical angle of a certain medium is `sin ^(-1)((3)/(5))`. The polarizing angle of the medium is :

Options

A. `sin^(-1)((4)/(5))`
B. `tan^(-1)((5)/(3))`
C. `tan^(-1)((3)/(4))`
D. `tan^(-1)((4)/(3))`

Answer

To solve the problem, we need to find the polarizing angle of a medium given its critical angle. The critical angle (C) is given as \( \sin^{-1} \left( \frac{3}{5} \right) \).

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between the polarizing angle (I) and the critical angle (C) is given by the formula:
\[ \tan I = \frac{1}{\sin C} \]

2. **Identify the Critical Angle**:
We know that:
\[ C = \sin^{-1} \left( \frac{3}{5} \right) \]

3. **Calculate \( \sin C \)**:
From the definition of the inverse sine function, we have:
\[ \sin C = \frac{3}{5} \]

4. **Substitute into the Formula**:
Now, substituting \( \sin C \) into the relationship:
\[ \tan I = \frac{1}{\sin C} = \frac{1}{\frac{3}{5}} = \frac{5}{3} \]

5. **Find the Polarizing Angle**:
To find the polarizing angle (I), we take the inverse tangent:
\[ I = \tan^{-1} \left( \frac{5}{3} \right) \]

6. **Conclusion**:
Thus, the polarizing angle of the medium is:
\[ I = \tan^{-1} \left( \frac{5}{3} \right) \]

### Final Answer:
The polarizing angle of the medium is \( \tan^{-1} \left( \frac{5}{3} \right) \).