Problem 31 - Arihant AIEEE Physics

Question

In a prism a ray deviates towards: (a) base of prism (b) refracting edge of a prism (c) normal to the base (d) second phase of the prism

Step-by-Step Solution

Answer

(a) base of prism

Step 1: Understanding the Prism

A prism is a transparent optical element with flat, polished surfaces that refract light. The fundamental property of a prism is the refraction of light, which occurs when light enters and exits at different angles due to the change in medium.

Step 2: Identifying the Light Path

When a ray of light enters a prism, it bends towards the normal due to refraction. As it exits the prism, it bends again at the second interface. The overall deviation of the ray is influenced by the angles of refraction at both interfaces.

Step 3: Determining the Direction of Deviation

In prisms, the light ray attempts to minimize the path and deviates towards the thicker part of the prism. The base of the prism is thicker compared to the refracting edge.

Step 4: Finalizing the Answer

Given the options, the ray tends to deviate towards the base of the prism, as the base is where the angle for internal deviation is minimized, and the light ray bends towards it within the prism.

Key Concepts

Refraction of Light

Refraction occurs when light travels through different media, causing it to change direction. This happens because there is a difference in the density of the media. Light slows down or speeds up as it passes through materials like glass or water compared to air. This change in speed bends the light wave.
The refraction is governed by Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of the velocities in the two media. This is expressed as:
\( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \)
where:

• \( n_1 \) and \( n_2 \) are the refractive indices of the first and second media respectively.
• \( \theta_1 \) is the incident angle, and \( \theta_2 \) is the refracted angle.

This principle explains why a straw in a glass of water appears bent. The light bending at the water interface is similar to how light behaves when it goes through a prism.

Optical Prism Behavior

An optical prism is a transparent object with flat surfaces that refract light. It has at least two non-parallel surfaces, which cause light to bend when it passes through. Prisms are usually made from glass or other transparent materials.
Prisms have unique properties due to their shape:

• Refraction at Entry: As light enters the prism, it refracts, bending towards the normal. This is the initial refraction.
• Internal Travel: The light then travels inside the prism, deviating towards the base because this is the path with minimal resistance.
• Refraction at Exit: When light exits, it refracts again, bending away from the normal. This second refraction contributes to the overall bending angle.

Prisms can separate white light into its component colors because different wavelengths refract at slightly different angles. This phenomenon is known as dispersion.

Deviation of Light Ray

The deviation of a light ray in a prism is the angle at which the light emerges compared to its original path. Light undergoes bending, first as it enters the prism and then as it exits. The overall deviation is the sum of these refractions.
The deviation angle is affected by:

• Angle of Incidence: How steeply the light hits the prism influences how much it deviates.
• Prism Angle: The angle between the two refracting surfaces of the prism plays a crucial role in determining deviation.
• Refractive Index: Higher indices cause greater bending of the light.

In general, the ray will bend towards the thicker side of the prism, which is why light typically deviates towards the base. This behavior can be used in various optical applications like cameras and other imaging instruments.