As seen from the figure

The angle between the incident ray and the
refracted ray = Angle of incidence+angle of reflection+90 degree=57.5+57.5+90=205 degree

Introduction:
When light passes from one medium to another, it undergoes refraction. The angle at which the incident light ray is polarized is known as the polarizing angle. In this scenario, light is incident on a glass surface at a polarizing angle of 57.5 degrees. We need to determine the angle between the incident ray and the refracted ray.

Explanation:
To understand the concept, we need to consider Snell's law, which describes the relationship between the angles of incidence and refraction:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
n1 = refractive index of the initial medium (air/vacuum = 1)
n2 = refractive index of the second medium (glass)
θ1 = angle of incidence
θ2 = angle of refraction

Step 1: Determine the refractive index of glass.
The refractive index of glass varies depending on the type of glass. For simplicity, let's assume it to be 1.5.

Step 2: Calculate the angle of refraction.
Using Snell's law, we can rearrange the equation to solve for θ2:

sin(θ2) = (n1 * sin(θ1)) / n2

Plugging in the values:
sin(θ2) = (1 * sin(57.5)) / 1.5
θ2 = sin^(-1)((1 * sin(57.5)) / 1.5)

Step 3: Calculate the angle between the incident and refracted rays.
The angle between the incident ray and the refracted ray can be found by subtracting the angle of refraction from the angle of incidence:

Angle between incident and refracted rays = θ1 - θ2

Plugging in the values:
Angle between incident and refracted rays = 57.5 - θ2

Step 4: Calculate the value of θ2 and the final result.
Using a scientific calculator, we can calculate the value of θ2, which comes out to be approximately 29.8 degrees.

Finally, substituting this value into the expression for the angle between the incident and refracted rays:
Angle between incident and refracted rays = 57.5 - 29.8
Angle between incident and refracted rays ≈ 27.7 degrees

Conclusion:
The angle between the incident ray and the refracted ray is approximately 27.7 degrees, not 205 degrees as mentioned in the question.