Explanation:

When light passes from one medium to another, it can undergo reflection, refraction, or both. The behavior of light at the interface between two media can be understood using Snell's law and the principle of total internal reflection.

Snell's Law:
Snell's law relates the angle of incidence (θ1), the angle of refraction (θ2), and the refractive indices (n1 and n2) of the two media. It can be stated as:

n1 * sin(θ1) = n2 * sin(θ2)

where n1 and n2 are the refractive indices of the initial and final media, respectively.

Reflection and Polarization:
When light is incident on a surface, it can be partially reflected and partially refracted. The reflected light can be partially or completely polarized, depending on the angle of incidence. For a particular angle of incidence, called the Brewster's angle, the reflected beam is completely polarized.

Angle of Refracted Beam:
In this scenario, the incident light is unpolarized and is incident from dry air (n=1) to a glass plate (n=1.52). Let's assume that the angle of incidence is θ1 and the angle of refraction is θ2.

Since the reflected beam is linearly polarized, it means that the incident light is incident at the Brewster's angle. At the Brewster's angle, the reflected light is completely polarized perpendicular to the plane of incidence.

Using Snell's law, we can write:

n1 * sin(θ1) = n2 * sin(θ2)

Substituting the values, we get:

1 * sin(θ1) = 1.52 * sin(90° - θ2)

Since the light is incident from air to glass, the angle of refraction can be calculated as:

θ2 = arcsin(sin(θ1) / 1.52)

This equation gives the angle of the refracted beam with respect to the surface normal.

Conclusion:
In this scenario, the angle of the refracted beam with respect to the surface normal can be calculated using Snell's law. The incident light is incident at the Brewster's angle, which results in a completely polarized reflected beam. The angle of the refracted beam can be calculated using the equation θ2 = arcsin(sin(θ1) / 1.52).