A beam of light travelling in water strikes a glass plate, which is also immersed in water. When the angle of incidence is ` 51^@`, the reflected beam is found to be plane polarised . What is the refractive index of glass if the refractive index of water is `(4)/3`? `[tan 51^(@)=1.235]`

Options

A. 1.605
B. 1.305
C. 1.33
D. 1.805

Answer

To find the refractive index of glass when a beam of light traveling in water strikes a glass plate immersed in water and the reflected beam is plane polarized, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Angle of incidence (i) = 51°
- Refractive index of water (μ_water) = 4/3
- We need to find the refractive index of glass (μ_glass).

2. **Understanding Plane Polarization:**
- The reflected beam is plane polarized when it reflects at the Brewster's angle (i_p). According to Brewster's law, the tangent of the Brewster's angle is given by:
\[ \tan(i_p) = \frac{\mu_{glass}}{\mu_{water}} \]

3. **Substituting the Known Values:**
- Since the angle of incidence is given as 51°, we can substitute this into the equation:
\[ \tan(51°) = \frac{\mu_{glass}}{\mu_{water}} \]

4. **Rearranging the Equation:**
- Rearranging the equation to solve for μ_glass gives us:
\[ \mu_{glass} = \tan(51°) \times \mu_{water} \]

5. **Calculating tan(51°):**
- From the problem, we know that:
\[ \tan(51°) = 1.235 \]

6. **Substituting Values:**
- Now substitute the values into the equation:
\[ \mu_{glass} = 1.235 \times \frac{4}{3} \]

7. **Performing the Calculation:**
- Calculate the value:
\[ \mu_{glass} = 1.235 \times 1.3333 \approx 1.647 \]

8. **Final Result:**
- Therefore, the refractive index of glass (μ_glass) is approximately 1.647.

### Conclusion:
The refractive index of glass is approximately **1.647**.