A light of wavelength fall on a plane surface at an angle of incidence 53. The refractive index of surface material, if the reflected light is completely plane polarised is

Options

A. `mu= 4/3`
B. `mu=4/5`
C. `mu=3/5`
D. `mu=5/3`

Answer

To solve the problem, we need to determine the refractive index of a surface material when light is incident at an angle of 53 degrees and the reflected light is completely plane polarized. We will use Brewster's Law for this purpose.

### Step-by-Step Solution:

1. **Understand Brewster's Law**: Brewster's Law states that the refractive index (μ) of a material is equal to the tangent of the angle of incidence (ip) at which light is completely polarized upon reflection. Mathematically, it is expressed as:
\[ \mu = \tan(ip) \]

2. **Identify the Given Information**:
- Angle of incidence (ip) = 53 degrees.
- We need to find the refractive index (μ).

3. **Apply Brewster's Law**:
- Substitute the angle of incidence into Brewster's Law:
\[ \mu = \tan(53^\circ) \]

4. **Calculate the Tangent**:
- We need to find the value of \(\tan(53^\circ)\). From trigonometric tables or a calculator:
\[ \tan(53^\circ) \approx 1.327 \]

5. **Final Calculation**:
- Thus, the refractive index of the surface material is:
\[ \mu \approx 1.327 \]

### Conclusion:
The refractive index of the surface material, when the reflected light is completely plane polarized at an angle of incidence of 53 degrees, is approximately 1.327.