Question

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is \(60^{\circ}\) ). In the position of minimum deviation, the angle of refraction will be (A) \(30^{\circ}\) for both the colours (B) greater for the violet colour (C) greater for the red colour (D) equal but not \(30^{\circ}\) for both the colours

Short answer

The angle of refraction will be 30 degrees for both red and violet colours in the position of minimum deviation.

Step-by-step solution

Understanding the concept of minimum deviation

When light passes through a prism at the angle of minimum deviation, the angle of incidence is equal to the angle of emergence, and the refracted ray inside the prism is parallel to the base of the prism. This implies that at minimum deviation, the angle of refraction (r) is equal to half the prism's angle (A), because the sum of angles in the triangle formed by the incident and emergent rays and the base of the prism inside must add up to 180 degrees.

Applying the concept to the prism angle

Given that the angle of the prism (A) is 60 degrees, we know from the concept of minimum deviation that the angle of refraction (r) will be half of that. Thus, r = A/2 = 60 degrees / 2 = 30 degrees.

Concluding the angle of refraction for both colors

Since the angle of refraction at minimum deviation is independent of the color of the light, both red and violet light will have the same angle of refraction of 30 degrees. Therefore, the angle of refraction will be 30 degrees for both the colours.

Key concepts

Angle of Refraction

When light travels from one medium to another, such as air entering a glass prism, it changes direction; this phenomenon is known as refraction. The angle at which the light beam bends is referred to as the angle of refraction. It is influenced by the indexes of refraction of the two media and the angle of incidence using Snell's Law. During the scenario of minimum deviation in a prism, the angle of refraction can be simply found as it is related to the prism's geometry.

For a prism in the position of minimum deviation, the angle of incidence is equal to the angle of emergence. This special case dictates that the refracted ray inside the prism is parallel to the base, creating an isosceles triangle with the prism's refracting surfaces. Therefore, for a symmetrical passage of light through the prism, the angle of refraction is exactly half of the prism's vertex angle. This holds true regardless of the wavelength or color of the incident light, allowing us to conclude that for a prism with a vertex angle of 60 degrees, the angle of refraction at minimum deviation will be 30 degrees.

Prism Angle

A prism is a transparent optical element with flat, polished surfaces that refract light. The most important characteristic of a prism in the context of light refraction is the prism angle, also known as the vertex angle. This is the angle between the two plane faces of the prism that are used to refract the light. The amount of bending that light undergoes inside the prism is largely dependent on this angle.

In the exercise provided, we consider a prism with a vertex angle of 60 degrees. Using our understanding of the principles of minimum deviation, we ensured that the calculations are based on the intrinsic properties of the prism. Since the prism angle is a fixed physical property, it offers a reliable starting point for various computations regarding the refraction and dispersion of light through the prism. It's important for students to comprehend that the prism angle plays a crucial role in determining the path of the light beam inside the prism and influences how the light is dispersed upon emerging.

Light Dispersion in Prism

The concept of light dispersion involves the splitting of white light into its constituent colors, a process commonly observed when light passes through a prism. This phenomenon occurs due to the variation in the refraction of different wavelengths of light, as each color has a unique refractive index within the prism's material. Violet light bends the most while red light bends the least, which is why we see a spectrum of colors emerge from the prism.

The question from the exercise is specifically about the position of minimum deviation, which is a unique angle where all wavelengths emerge at the same angle. It is worth noting that although dispersion separates the colors, this state of minimum deviation means that the refracted angles will be the same for both red and violet light when assessed individually under this condition. However, outside of this specific condition, if we were to measure different colors individually without considering minimum deviation, we would expect to find that the angle of refraction would vary for each color due to their different speeds in the prism material.