Table of Contents

## Introduction

The **refractive index (n)** of a medium is a measure of how much light slows down when passing through it, compared to the speed of light in a vacuum. It is a dimensionless quantity.

It expresses the relationship that when light passes from one medium to another, its direction changes due to the change in speed. The amount of bending, or refraction, depends on the refractive indices of the two mediums and the angles of incidence and refraction.

The **refraction formula** is widely used in optics and is crucial in understanding the behavior of light as it interacts with different mediums, such as when light passes from air to water or from air to a glass lens.

## Formula for Refraction

The refraction formula describes the relationship between the angles of incidence and refraction when light passes through a boundary between two different transparent mediums. It is known as Snell’s law of refraction and is given by the formula:

**n1 x sin(θ1) = n2 x sin(θ2) **

where:

n1 is the refractive index of the medium the incident ray is coming from,

n2 is the refractive index of the medium the refracted ray enters,

θ1 is the angle of incidence (measured between the incident ray and the normal to the boundary),

θ2 is the angle of refraction (measured between the refracted ray and the normal to the boundary).

## What is Refraction Formula mathematically?

Consider a ray of light travelling from medium 1 to medium 2. Let the angle of incidence be *i *and the angle of refraction be r. Let the speed of light in medium 1 be v1 and that in medium 2 be v2. Let n21 be the refractive index of medium 2 with respect to medium 1.

Light travelling from medium 1 to medium 2

Then, according to Snell’s law,

Also, by definition of refractive index,

Thus, from statement (i) and (ii),

Let n1 and n2 be the absolute refractive indices of medium 1 and medium 2 respectively. If the velocity of light in vacuum is *c, *then,

From statements (iii) and (iv), Snell’s law can be expressed as

Remember that the refractive index does not have a unit as it is just a ratio of similar quantities.

## Solved Examples on Refraction Formula

**Example 1: A light ray travels from water (refractive index = 1.33) into diamond (refractive index = 2.42). If the angle of incidence is 40 degrees, calculate the angle of refraction. **

**Solution: **

Given:

n₁ (refractive index of water) = 1.33

n₂ (refractive index of diamond) = 2.42

θ₁ (angle of incidence) = 40 degrees

Using Snell’s law we can write,

n₁ x sin(θ₁) = n₂ x sin(θ₂)

Substituting the given values:

1.33 x sin(40) = 2.42 x sin(θ₂)

sin(θ₂) = (1.33 x sin(40)) / 2.42

sin(θ₂) ≈ 0.706

Taking the inverse sine (arcsine) of both sides:

θ₂ = arcsine(0.706)

Using a calculator:

θ₂ ≈ 44.1 degrees

Therefore, the angle of refraction is approximately 44.1 degrees.

**Example 2: Light enters from air to glass having a refractive index of 1.50. What is the speed of light in glass? (The speed of light in vacuum = 3 × 108 m/s). **

**Answer:** To calculate the speed of light in glass, we can use the formula:

Speed of light in medium = Speed of light in vacuum / Refractive index of the medium

Given: Speed of light in vacuum (c) = 3 × 108 m/s Refractive index of glass (n) = 1.50

Substituting the values into the formula:

Speed of light in glass = (3 × 108 m/s) / 1.50

Speed of light in glass ≈ 2 × 108 m/s

Therefore, the speed of light in glass is approximately 2 × 108 m/s.

## FAQs on Refraction Formula

### What is the general formula for refraction?

The general formula for refraction is known as Snell's law. It relates the angles of incidence and refraction of a light ray passing through the boundary between two different transparent mediums. Snell's law is expressed as: n1 x sin(θ1) = n2 x sin(θ2) where: n1 is the refractive index of the medium the incident ray is coming from, n2 is the refractive index of the medium the refracted ray enters, θ1 is the angle of incidence (measured between the incident ray and the normal to the boundary), θ2 is the angle of refraction (measured between the refracted ray and the normal to the boundary). The refractive index (n) of a medium is a measure of how much light slows down when passing through it, compared to the speed of light in a vacuum. It is a dimensionless quantity.

### What are the 2 laws of refraction?

Laws of refraction are: The incident ray, the refracted ray, and the normal at the point of incidence lie on the same plane. The refractive index of a refractive medium with respect to the incident medium is equal to the ratio of the sine of the incident angle to the sine of the refractive angle. This is also known as Snell's law.

### What is the relationship between the angles of incidence and refraction?

The relationship between the angles of incidence and refraction is given by Snell's law. It states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.

### What is the mathematical expression of Snell's law?

Snell's law is expressed as: n₁ x sin(θ₁) = n₂ x sin(θ₂), where n₁ and n₂ are the refractive indices of the incident and refracting media, respectively, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.

### What is Snell's law?

Snell's law, also known as Snell-Descartes law, is a fundamental principle in optics that describes the behavior of light as it passes from one medium to another. It relates the angles of incidence and refraction to the refractive indices of the two media involved.

### What is refraction in physics?

Refraction in physics refers to the bending or change in direction of a wave as it passes from one medium to another, caused by a change in its speed. It occurs due to the difference in the optical density or refractive index of the two mediums. Refraction is responsible for phenomena such as the bending of light in lenses, the formation of rainbows, and the apparent displacement of objects in water.