Light is incident on a glass surface at polarising angle of `57.5^(@)` Then the angle between the incident ray and the refracted ray is

Options

A. `57.5^(@)`
B. `115^(@)`
C. `205^(@)`
D. `145^(@)`

Explanation

To solve the problem, we need to find the angle between the incident ray and the refracted ray when light is incident on a glass surface at a polarizing angle of 57.5 degrees.

### Step-by-Step Solution:

1. **Understand 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. **Identify the Given Data**:
- Polarizing angle (θ_p) = 57.5 degrees.

3. **Use the Relationship Between Angles**:
- At the polarizing angle, the angle between the reflected ray and the refracted ray is 90 degrees. This means that if we denote:
- θ_i = angle of incidence (57.5 degrees),
- θ_r = angle of reflection (also 57.5 degrees),
- θ_t = angle of refraction,
then we have:
\[ θ_r + θ_t = 90^\circ \]

4. **Calculate the Angle of Refraction**:
- Since θ_r = 57.5 degrees, we can find θ_t:
\[ θ_t = 90^\circ - θ_r = 90^\circ - 57.5^\circ = 32.5^\circ \]

5. **Find the Angle Between Incident Ray and Refracted Ray**:
- The angle between the incident ray and the refracted ray is the sum of the angle of incidence and the angle of refraction:
\[ \text{Angle between incident ray and refracted ray} = θ_i + θ_t = 57.5^\circ + 32.5^\circ = 90^\circ \]

### Final Answer:
The angle between the incident ray and the refracted ray is **90 degrees**.