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))`

Explanation

To find the polarizing angle of the medium given its critical angle, we can follow these steps:

### Step 1: Understand the relationship between critical angle and polarizing angle
The polarizing angle (θp) is related to the critical angle (θc) through Brewster's law. According to Brewster's law, the tangent of the polarizing angle is equal to the reciprocal of the sine of the critical angle:
\[ \tan(\theta_p) = \frac{1}{\sin(\theta_c)} \]

### Step 2: Identify the critical angle
The critical angle is given as:
\[ \theta_c = \sin^{-1}\left(\frac{3}{5}\right) \]

### Step 3: Calculate the sine of the critical angle
From the given critical angle, we find:
\[ \sin(\theta_c) = \frac{3}{5} \]

### Step 4: Substitute into Brewster's law
Now we can substitute this value into the equation for the polarizing angle:
\[ \tan(\theta_p) = \frac{1}{\sin(\theta_c)} = \frac{1}{\frac{3}{5}} = \frac{5}{3} \]

### Step 5: Find the polarizing angle
To find the polarizing angle, we take the arctangent:
\[ \theta_p = \tan^{-1}\left(\frac{5}{3}\right) \]

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