Problem 38 - Arihant AIEEE Physics

Question

The refractive index of the material of prism, if a thin prism of angle \(A=6^{\circ}\), produces a deviation \(\delta=3^{\circ}\), is: (a) \(1.5\) (b) \(1.2\) (c) \(1.1\) (d) \(1.25\)

Step-by-Step Solution

Answer

The refractive index is 1.5, so the answer is (a) 1.5.

Step 1: Understand the Prism Formula

The formula for deviation produced by a thin prism is given by \( \delta = (n - 1)A \), where \( \delta \) is the deviation angle, \( n \) is the refractive index, and \( A \) is the prism angle. Here, \( \delta = 3^{\circ} \) and \( A = 6^{\circ} \).

Step 2: Rewrite the Formula to Solve for Refractive Index

We need to find the refractive index \( n \). Rearrange the formula to solve for \( n \): \( n = 1 + \frac{\delta}{A} \).

Step 3: Plug in the Values

Substitute the given values into the formula: \( n = 1 + \frac{3^{\circ}}{6^{\circ}} \).

Step 4: Calculate the Refractive Index

Perform the calculation: \( n = 1 + \frac{3}{6} = 1 + 0.5 = 1.5 \).

Key Concepts

Prism Formula

The prism formula is a pivotal equation in optics, especially when dealing with thin prisms. This formula is used to determine the angle of deviation a light ray undergoes when passing through a prism. For a thin prism, the deviation angle, \( \delta \), is expressed as \( \delta = (n - 1)A \). Here, \( n \) represents the refractive index, while \( A \) symbolizes the prism angle.

This equation is simple yet powerful. It helps us understand how different materials bend light differently depending on their refractive index. This is why the refractive index is important; it tells us how much the light will deviate. The prism formula is particularly useful in scenarios where the angles involved are small, allowing for straightforward calculations.

Angle of Deviation

The angle of deviation is a key concept in optics. It indicates how much a light ray shifts direction after passing through a prism. In simple terms, it's the angle between the incoming light ray and the outgoing ray. For a thin prism, this angle is influenced by both the prism angle \( A \) and the refractive index \( n \) of the material.

Understanding angle of deviation is crucial because it helps in designing lenses and optical devices. It allows us to predict and manipulate how light behaves, making it a foundational element in optical engineering. Knowing the deviation can help in multiple applications like creating prisms for scientific instruments or even in corrective lenses for glasses.

Optics

Optics is a branch of physics dedicated to studying light and its interactions with different materials. It encompasses a wide range of phenomena including reflection, refraction, and dispersion. Refraction is crucial in optics as it explains how light bends when transitioning between different mediums.

In the context of prisms, optics teaches us how light changes its path inside a solid prism due to variations in speed. This bending of light is dictated by the refractive index of the material. The governing principles of optics help design various tools like binoculars, cameras, and even complex instruments used in scientific research.

Thin Prism

A thin prism is a type of optical prism characterized by its very small prism angle. This allows for simpler analysis using linear approximations. When dealing with thin prisms, angles like deviation and refraction are small, making calculations using the prism formula quite manageable.

Thin prisms are extensively used in education and simple experiments due to their predictability and ease of use. They help students and scientists alike to understand fundamental concepts of light behavior without the complexities introduced by thicker or more angular prisms. Thin prisms are practical for applications where high precision is not crucial, but understanding of primary principles is needed.