Refraction of Light Through a Glass Prism

This section covers the phenomenon of the refraction of light specifically as it passes through a prism made of glass.
A glass prism is a transparent optical element with flat, polished surfaces that refract light. At least two of the flat surfaces must have an angle between them. The most common shape is the triangular prism, which has a triangular base and three rectangular lateral surfaces.

Refracting Surfaces: The two plane surfaces of the prism through which the light enters and leaves are known as the refracting surfaces.
Refracting Edge: The line along which the two refracting surfaces meet is called the refracting edge of the prism.
Base of the Prism: The surface opposite the refracting edge is called the base of the prism.
Angle of the Prism ( $A$ ): The angle between the two refracting surfaces is defined as the angle of the prism or the refracting angle. It is denoted by the symbol $A$ .
Principal Section: Any section of the prism that is perpendicular to its refracting edge is called the principal section. This is typically represented as a triangle in ray diagrams.

When a ray of light enters the glass prism, it undergoes refraction twice—once at the point of entry (the first refracting surface) and once at the point of exit (the second refracting surface).
Incident Ray: The ray of light that falls upon the first refracting surface of the prism.
Refracted Ray: As the light enters the glass from the air, it slows down and bends toward the normal. This ray traveling inside the prism is the refracted ray.
Emergent Ray: As the light exits the glass and enters the air at the second refracting surface, it speeds up and bends away from the normal. This final ray is called the emergent ray.

Angle of Incidence ( $i$ ): The angle between the incident ray and the normal at the first refracting surface.
Angle of Refraction ( $r_1$ ): The angle between the refracted ray and the normal inside the prism at the first surface.
Second Angle of Refraction ( $r_2$ ): The angle between the refracted ray and the normal inside the prism at the second surface (sometimes treated as the angle of incidence for the second surface).
Angle of Emergence ( $e$ ): The angle between the emergent ray and the normal at the second refracting surface.
Angle of Deviation ( $\delta$ ): This is the unique angle formed between the direction of the original incident ray (extended forward) and the direction of the emergent ray (extended backward). It represents the total amount the light ray has been bent by the prism.

For any prism, the following relationship holds true regarding the angle of the prism and the internal angles of refraction: $A = r_1 + r_2$
The relationship between the angle of incidence ( $i$ ), the angle of emergence ( $e$ ), the angle of the prism ( $A$ ), and the angle of deviation ( $\delta$ ) is given by: $A + \delta = i + e$
Rearranging this to solve for the angle of deviation: $\delta = (i + e) - A$

As the angle of incidence ( $i$ ) is varied, the angle of deviation ( $\delta$ ) changes. There is a specific angle of incidence where the angle of deviation reaches its minimum value, known as the Angle of Minimum Deviation ( $\delta_m$ ).
At the position of minimum deviation, the following conditions are met: - The angle of incidence is equal to the angle of emergence ( $i = e$ ). - The refracted ray inside the prism is parallel to the base of the prism (provided the prism is isosceles or equilateral). - The internal refraction angles are equal ( $r_1 = r_2 = r$ ).
Using these conditions, the refractive index ( $n$ ) of the glass material can be calculated using the prism formula: $n = \frac{\sin(\frac{A + \delta_m}{2})}{\sin(\frac{A}{2})}$

When a beam of white light enters a glass prism, it is not only refracted but also split into its constituent colors (red, orange, yellow, green, blue, indigo, and violet). This phenomenon is known as dispersion.
This occurs because different colors of light (different wavelengths) travel at different speeds in glass and therefore have different refractive indices ( $n$ ).
Red Light: Has the longest wavelength and is refracted the least, resulting in the smallest angle of deviation.
Violet Light: Has the shortest wavelength and is refracted the most, resulting in the largest angle of deviation.