A ray of light is incident on the surface of plate of glass of refractive index `1.5` at the polarising angle. The angle of refraction of the ray will be

Options

A. `33.7^(@)`
B. `23.7^(@)`
C. `43.7^(@)`
D. `53.7^(@)`

Explanation

To find the angle of refraction when a ray of light is incident on a glass plate at the polarizing angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Polarizing Angle**:
The polarizing angle (Ip) is defined by Brewster's Law, which states that at this angle, the reflected and refracted rays are perpendicular to each other. The relationship is given by:
\[ \tan(I_p) = \mu \]
where \( \mu \) is the refractive index of the medium.

2. **Given Data**:
The refractive index of glass \( \mu = 1.5 \).

3. **Calculate the Polarizing Angle (Ip)**:
Using Brewster's Law:
\[ I_p = \tan^{-1}(\mu) = \tan^{-1}(1.5) \]
Using a calculator, we find:
\[ I_p \approx 56.3^\circ \]

4. **Use the Relationship Between Polarizing Angle and Angle of Refraction**:
According to the relationship between the polarizing angle and the angle of refraction (R):
\[ I_p + R = 90^\circ \]
Rearranging gives:
\[ R = 90^\circ - I_p \]

5. **Substitute the Value of Ip**:
Now substituting the value of \( I_p \):
\[ R = 90^\circ - 56.3^\circ = 33.7^\circ \]

6. **Conclusion**:
The angle of refraction (R) when the ray of light is incident at the polarizing angle is:
\[ R \approx 33.7^\circ \]

### Final Answer:
The angle of refraction of the ray will be approximately **33.7 degrees**.