Explanation:

To find the displacement of the rays due to passage through the glass plate, we need to consider the phenomenon of total internal reflection.

1. Angle of Incidence and Angle of Total Internal Reflection:
When a ray of light passes from a medium of lower refractive index (such as air) to a medium of higher refractive index (such as glass), it bends towards the normal. The angle between the incident ray and the normal is called the angle of incidence.

As the angle of incidence increases, the refracted ray bends more and approaches the boundary between the two media. At a certain critical angle, the refracted ray becomes parallel to the boundary and does not leave the medium. This critical angle is known as the angle of total internal reflection.

2. Total Internal Reflection:
In the case of total internal reflection, the refracted ray is not transmitted into the second medium (glass) but is instead reflected back into the first medium (air). This phenomenon occurs when the angle of incidence exceeds the critical angle.

3. Displacement of Rays:
When a ray of light undergoes total internal reflection, it changes its direction. In the case of a glass plate, this change in direction occurs twice - once when the ray enters the glass plate and once when it exits.

The displacement of the ray due to passage through the glass plate can be calculated using the formula:

Displacement (R) = 2t * tan(θ)

Where:
- R is the displacement of the ray
- t is the thickness of the glass plate
- θ is the angle of incidence (equal to the angle of total internal reflection)

4. Refractive Index of Glass:
The refractive index of a material is a measure of how much the speed of light is reduced when it travels through that material. It is denoted by the symbol "n". In the case of glass, the refractive index (n) is greater than 1, indicating that light slows down when it enters the glass.

The refractive index is related to the angle of incidence and the angle of refraction by Snell's law:

n = sin(θ1) / sin(θ2)

Where:
- θ1 is the angle of incidence
- θ2 is the angle of refraction

In the case of total internal reflection, the angle of refraction is 90 degrees, and sin(90) = 1. Therefore, the refractive index can also be written as:

n = sin(θc) / sin(90)

Where θc is the critical angle.

Summary:
- When a ray of light passes from air to glass, it bends towards the normal.
- Total internal reflection occurs when the angle of incidence exceeds the critical angle.
- The displacement of the ray due to passage through the glass plate can be calculated using the formula R = 2t * tan(θ), where t is the thickness of the glass plate and θ is the angle of incidence.
- The refractive index of glass (n) is greater than 1, indicating that light slows down when it enters the glass.
- The refractive index is related to the angle of incidence and the angle of refraction by Snell's law. In the case of total internal reflection, the angle of refraction is 90 degrees.
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