If the polarising angle for a given medium is ` 60^@`, then the refractive index of the medium is

Options

A. `(1)/(sqrt(3))`
B. `sqrt((3)/(2))`
C. `1`
D. `sqrt(3)`

Explanation

To find the refractive index of a medium when the polarizing angle is given, we can use Brewster's law. Here’s a step-by-step solution:

### Step 1: Understand Brewster's Law
Brewster's law states that the refractive index (n) of a transparent medium is equal to the tangent of the polarizing angle (IP). This can be expressed mathematically as:
\[ n = \tan(IP) \]

### Step 2: Identify the Given Information
From the question, we know:
- The polarizing angle \( IP = 60^\circ \)

### Step 3: Apply Brewster's Law
Using Brewster's law, we can substitute the value of the polarizing angle into the equation:
\[ n = \tan(60^\circ) \]

### Step 4: Calculate the Tangent of the Angle
The tangent of \( 60^\circ \) is a known trigonometric value:
\[ \tan(60^\circ) = \sqrt{3} \]

### Step 5: Substitute the Value
Now, substituting this value back into the equation for the refractive index:
\[ n = \sqrt{3} \]

### Step 6: Conclusion
Thus, the refractive index of the medium is:
\[ n = \sqrt{3} \]

### Final Answer
The refractive index of the medium is \( \sqrt{3} \).

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