The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refraction index n ) is

Options

A. `sin^(-1) (n)`
B. `sin^(-1) ((1)/(n))`
C. `tan^(-1)((1)/(n))`
D. `tan^(-1)(n)`

Answer

To find the angle of incidence at which reflected light is totally polarized when light reflects from air to glass (with a refractive index \( n \)), we can use Brewster's Law. Here’s the step-by-step solution:

### Step 1: Understand Brewster's Law
Brewster's Law states that the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection, is known as Brewster's angle (\( i_p \)). At this angle, the reflected light is completely polarized.

### Step 2: Write the formula from Brewster's Law
According to Brewster's Law, the tangent of Brewster's angle is equal to the refractive index of the second medium (in this case, glass) relative to the first medium (in this case, air). The formula is given by:

\[ \tan(i_p) = n \]

where \( n \) is the refractive index of the glass.

### Step 3: Solve for Brewster's angle
To find the angle of incidence (\( i_p \)), we take the arctangent (inverse tangent) of both sides:

\[ i_p = \tan^{-1}(n) \]

### Step 4: Conclusion
Thus, the angle of incidence at which the reflected light is totally polarized when light reflects from air to glass is:

\[ i_p = \tan^{-1}(n) \]

### Final Answer
The angle of incidence at which reflected light is totally polarized is \( \tan^{-1}(n) \).

---