At what angle of incidence will the light reflected from liquid `(mu = 1.732)` be completely polarised. Does this angle depend on the wavelength of light ?

Options

A. `53^(@)`
B. `60^(@)`
C. `30^(@)`
D. `42^(@)`

Explanation

To determine the angle of incidence at which light reflected from a liquid (with a refractive index \( \mu = 1.732 \)) is completely polarized, we will use Brewster's Law.

### Step-by-Step Solution:

1. **Understanding Brewster's Law**:
Brewster's Law states that the angle of incidence \( \theta_B \) at which light is completely polarized upon reflection is given by the formula:
\[ \mu = \tan(\theta_B) \]
where \( \mu \) is the refractive index of the medium.

2. **Substituting the Given Value**:
We are given that the refractive index \( \mu = 1.732 \). We can substitute this value into the equation:
\[ 1.732 = \tan(\theta_B) \]

3. **Calculating the Angle**:
To find \( \theta_B \), we take the arctangent (inverse tangent) of both sides:
\[ \theta_B = \tan^{-1}(1.732) \]

4. **Finding the Angle**:
We know that \( \tan(60^\circ) = 1.732 \). Therefore:
\[ \theta_B = 60^\circ \]

5. **Conclusion**:
The angle of incidence at which the light reflected from the liquid is completely polarized is \( 60^\circ \).

6. **Dependence on Wavelength**:
Now, we need to determine if this angle depends on the wavelength of light. The refractive index \( \mu \) can be expressed in terms of the speed of light in different media:
\[ \mu = \frac{c}{v} \]
where \( c \) is the speed of light in vacuum and \( v \) is the speed of light in the medium. The speed of light in a medium can be related to the wavelength \( \lambda \) and frequency \( f \) as:
\[ v = \lambda f \]
Since the refractive index \( \mu \) is inversely related to the wavelength \( \lambda \), we can conclude that:
\[ \mu \propto \frac{1}{\lambda} \]
Therefore, since \( \theta_B \) is directly related to \( \mu \), it also depends on the wavelength of light.

### Final Answer:
- The angle of incidence for complete polarization is \( 60^\circ \).
- Yes, this angle does depend on the wavelength of light.