# Refractive Index

The ratio between the speed of light in medium to speed in a vacuum is the refractive index. When light travels in a medium other than the vacuum, the atoms of that medium continually absorb and re-emit the particles of light, slowing down the speed light. In this article, let us discuss the refractive index of water and various mediums.

## What Is Refractive Index?

Refractive index is defined as

The ratio of the speed of light in a vacuum to its speed in a specific medium.

Refractive index is also referred to as refraction index or index of refraction. The speed of light in a medium depends on the properties of the medium. In electromagnetic waves, the speed is dependent on the optical density of the medium. Optical density is the tendency of the atoms in a material to restore the absorbed electromagnetic energy. The more optically dense material is, the slower the speed of light. One such indicator of the optical density of a medium is the refractive index.

## Refractive Index Formula

The refractive index is dimensionless. It is a number that indicates the number of times slower than a light wave would be in the material than it is in a vacuum. The refractive index, represented by symbol n, is the velocity of light in vacuum divided by the velocity of light in a medium. The formula of the refractive index is as follows:

 $$\begin{array}{l}n=\frac{c}{v}\end{array}$$

Where,

• n is the refractive index
• c is the velocity of light in a vacuum ( 3 × 108 m/s)
• v is the velocity of light in a substance

The vacuum has a refractive index of 1. The refractive index of other materials can be calculated from the above equation. Higher the refractive index, the higher the optical density and slower is the speed of light. The table below lists the refractive index of different media.

 Material Refractive Index Air 1.0003 Water 1.333 Diamond 2.417 Ice 1.31 Ethyl Alcohol 1.36

## Refractive Index Example

The refractive index of glass ng is 1.52 and refractive index of water nw is 1.33. Since the refractive index of glass is higher than the water, the speed of light in water is faster than the speed of light through glass. If the refractive index of a medium is greater than that of another, then the first medium is said to be optically denser. Most of the substances we know have a positive refractive index having value more than zero. The material will have a negative refractive index when it has negative permittivity and permeability.

The refractive index provides a measure of the relative speed of light in different media. Knowing the refractive indices of different media helps the student to identify the direction in which way the light would bend while passing from one medium to another.

### Why is High Refractive Index Important for Optical Polymers?

Optical polymers with high refractive index allow light rays to bend more within the material, which helps in lowering the profile of the lens. Also, as the refractive index increases, the thickness of the lens decreases, resulting in less weight.

### What is Refractive Index Gradient?

• The refractive index gradient is defined as the rate of change of refractive index with respect to distance in the material. Distance refers to the slope of the refractive index profile at any point.
• The refractive index gradient is expressed in terms of reciprocal of a unit of distance.
• An example of a refractive index gradient is the rate of change of refractive index at any point with respect to distance.
• The refractive index gradient is a vector point function.

### How Does The Refractive Index Vary with Wavelength?

According to the definition of the refractive index, the speed of light is the product of frequency and wavelength. The frequency of the light wave remains unchanged, irrespective of the medium. Whereas the wavelength of the light wave changes based on refraction. Hence, the refractive index varies with wavelength.

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## Frequently Asked Questions – FAQs

Q1

### What is refractive index?

The refractive index is the measure of bending of a light ray when passing from one medium to another. It can also be defined as the ratio of the velocity of a light ray in an empty space to the velocity of light in a substance, n = c/v.

Q2

### What is the refractive index of water?

The refractive index of water is 1.333.

Q3

### What is the formula to calculate the refractive index of a medium?

The refractive index of a medium can be calculated using the following formula:
n = c/v
where n is the refractive index of the medium
c is the velocity of light in vacuum
v is the velocity of light in the medium

Q4

### Is the speed of light faster in glass or water?

The speed of light is faster in water. The refractive index of water is 1.3 and the refractive index of glass is 1.5. From the equation n = c/v, we know that the refractive index of a medium is inversely proportional to the velocity of light in that medium. Hence, light travels faster in water.

Q5

### What is the refractive index of the medium in which the speed of light is 1.5 × 108 m/s?

The refractive index of the medium can be calculated using the formula:
n = c/v
Substituting the values in the equation, we get
n = 3 × 108 m/s/1.5 × 108 m/s = 2
The refractive index of the medium is 2.
The speed of light in an unknown medium is 1.76 × 108 m/s. Calculate the refractive index of the medium.
The refractive index of a medium is calculated by the formula:
n = c/v
where c is the speed of light in a vacuum.
v is the speed of light in the medium.
Substituting the values in the above equation, we get
n = (3 × 108)/(1.76 × 108) = 1.7045

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