Does the polarizing angle e, for a transparent medium depend upon the wavelength of light?

Answer

To determine whether the polarizing angle \( e \) for a transparent medium depends upon the wavelength of light, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Polarizing Angle**:
The polarizing angle, also known as Brewster's angle, is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection.

2. **Brewster's Law**:
Brewster's law states that the polarizing angle \( e \) is related to the refractive index \( \mu \) of the medium by the formula:
\[ \tan(e) = \mu \]
where \( e \) is the polarizing angle and \( \mu \) is the refractive index of the medium.

3. **Refractive Index Dependence on Wavelength**:
The refractive index \( \mu \) of a medium is known to depend on the wavelength of light. Generally, as the wavelength increases, the refractive index decreases. This relationship can be expressed as:
\[ \mu \propto \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength of light.

4. **Substituting into Brewster's Law**:
Since \( \tan(e) = \mu \), we can substitute the relationship of the refractive index with wavelength into Brewster's law:
\[ \tan(e) \propto \frac{1}{\lambda} \]
This implies that as the wavelength \( \lambda \) changes, the value of \( \tan(e) \) will also change.

5. **Conclusion**:
Therefore, since \( e \) is related to \( \tan(e) \), it follows that the polarizing angle \( e \) does indeed depend on the wavelength of light. As the wavelength changes, the polarizing angle will also change.

### Final Answer:
Yes, the polarizing angle \( e \) for a transparent medium does depend upon the wavelength of light.