From Brewster's law, except for polished metallic surfaces, the polarising angle

Options

A. depends on wavelength and si different for different colours
B. independent of wavelength and is different for different colours
C. independent of wavelength and is same for different colours
D. depends on wavelength and is same for different colours

Explanation

To solve the question regarding Brewster's law and the polarizing angle, we will follow these steps:

### Step 1: Understand Brewster's Law
Brewster's law states that the refractive index (n) of a medium is related to the polarizing angle (θp) by the equation:
\[ n = \tan(\theta_p) \]

### Step 2: Define the Variables
- **n**: Refractive index of the medium
- **θp**: Polarizing angle
- **c**: Speed of light in vacuum
- **v**: Speed of light in the medium
- **λ**: Wavelength of light in the medium
- **λ₀**: Wavelength of light in vacuum

### Step 3: Relate Refractive Index to Wavelength
The refractive index can also be expressed in terms of the speed of light:
\[ n = \frac{c}{v} \]
When considering wavelength, we can express the relationship as:
\[ n = \frac{\lambda_0}{\lambda_m} \]
where λm is the wavelength in the medium.

### Step 4: Substitute into Brewster's Law
Substituting the expression for n into Brewster's law gives:
\[ \frac{\lambda_m}{\lambda_0} = \tan(\theta_p) \]

### Step 5: Solve for the Polarizing Angle
From the above equation, we can express the polarizing angle as:
\[ \theta_p = \tan^{-1}\left(\frac{\lambda_m}{\lambda_0}\right) \]

### Step 6: Analyze the Dependence of θp
From the equation derived, we can conclude that the polarizing angle (θp) depends on the wavelength of light used (λm) and the wavelength in vacuum (λ₀). Since different colors of light have different wavelengths, the polarizing angle will vary with the color of light.

### Conclusion
Thus, the polarizing angle depends on the wavelength of the light used and will be different for different colors of light.