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 find the refractive index of the surface material given that the reflected light is completely plane polarized at an angle of incidence of 53 degrees.

### Step-by-Step Solution:

1. **Understand Brewster's Law**:
Brewster's Law states that the angle of incidence (θp) at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection, is given by:
\[ \mu = \tan(\theta_p) \]
where μ is the refractive index of the material and θp is the angle of incidence.

2. **Identify the Given Values**:
- Angle of incidence (I) = 53 degrees
- We need to find the refractive index (μ) of the surface material.

3. **Apply Brewster's Law**:
Since the reflected light is completely plane polarized, we can use Brewster's Law:
\[ \mu = \tan(53^\circ) \]

4. **Calculate the Tangent**:
Now, we need to find the value of \(\tan(53^\circ)\):
\[ \tan(53^\circ) \approx 1.327 \]
For practical purposes, we can round this to 1.33.

5. **Final Result**:
Therefore, the refractive index of the surface material is:
\[ \mu \approx 1.33 \]

6. **Convert to Fraction**:
The value 1.33 can also be expressed as a fraction:
\[ \mu = \frac{4}{3} \]

7. **Conclusion**:
The refractive index of the surface material is \( \frac{4}{3} \) or 1.33.