# Refraction & Dispersion

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The diagram shows different wavelengths of incident light approaching the boundary between air and glass.

• As each wavelength crosses the boundary into the glass it bends towards the normal (the dotted green line).
• Each incident wavelength is refracted towards the normal because it travels from air, the faster, less optically dense medium with a smaller refractive index into the glass, a slower, more optically dense medium with the higher refractive index.
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## Description

#### Refraction & Dispersion

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
As light travels from a fast medium such as air to a slow medium such as water it bends toward 'the normal' and slows down. As light passes from a slow medium such as diamond to a faster medium such as glass it bends away from 'the normal' and speeds up.
Yes! When light leaves a vacuum or travels from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.
Chromatic dispersion refers to the way that light separates into its component wavelengths (and so colours), under certain conditions.
Refraction refers to the way light changes speed and direction as it travels across the interface between one transparent medium to another.
Yes! When light leaves a vacuum or travels from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.

Have you already checked out An Introduction to Reflection, Refraction and Dispersion?

It is the opening page of our Reflection, Refraction and Dispersion Series and contains masses of useful information. This is the table of contents:

• This page looks at the refraction and chromatic dispersion of a ray of light containing six different wavelengths as they approach the boundary between air and glass.
• Related topics, including reflection, are covered on other pages of this series.
• Introductions to the terms refractive index and the law of refraction (sometimes called Snell’s law) also appear on later pages in the series.

An overview of refraction

• Refraction refers to the way that light (electromagnetic radiation) changes speed and direction as it travels from one transparent medium into another.
• Refraction takes place as light travels across the boundary between different transparent media and is a result of their different optical properties.
• Refraction is the result of the differences in the optical density of transparent media. Gases have a very low optical density whilst diamonds have a high optical density.
• When light is refracted its path bends and so changes direction.
• The effect of refraction on the path of a ray of light is measured by the difference between the angle of incidence and the angle of reflection.
• As light travels across the interface between different media it changes speed.
• Depending on the media through which light is refracted, its speed can either increase or decrease.

An overview of chromatic dispersion

• The term chromatic dispersion (often simply called dispersion) refers to the way that different wavelengths of light separate at the boundary between transparent media during the process of refraction.
• Dispersion causes the separate wavelengths present in a ray of light to fan out so that their corresponding colours become visible to an observer.
• When white light is dispersed, the spread of colours has red on one side and violet at the other.
• The colours produced by dispersion are spectral colours – ROYGBV.
• Dispersion occurs because refraction causes every wavelength of light to alter speed, and at the same time, to bend and change direction by a different amount.
• For dispersion to occur the incident light approaching the boundary between two different transparent media must contain a sufficiently wide range of wavelengths to enable them to separate out so that their associated colours are visible to an observer.
• A familiar example of dispersion is when white light strikes a prism and a rainbow of colours become visible to an observer.
• As light enters a prism it separates into its component wavelengths which an observer perceives as bands of colour.
• Colour is not a property of electromagnetic radiation, but a feature of visual perception experienced by an observer in the presence of different wavelengths of light.

An overview of refraction and wavelength

• Every wavelength of light is affected to a different degree when it encounters a medium and undergoes refraction.
• Every wavelength of light changes both speed and direction by a different amount when it encounters a new medium and undergoes refraction.
• The change in angle for any wavelength of light undergoing refraction within a specific transparent medium can be predicted if the refractive index of the medium is known.
• The refractive index for a medium is calculated by finding the difference between the speed of light in a vacuum and its speed as it travels through the medium.
• To understand dispersion we must recognise that the refractive index of a transparent medium must be corrected for different wavelengths of the visible spectrum.
Colour wavelength (nm) Refractive index
Red 640 1.50917
Yellow 589 1.51124
Green 509 1.51534
Blue 486 1.51690
Violet 434 1.52136

The refractive index for crown glass is often given as being 1.52.  This table shows how that figure alters with wavelength

The diagram

• The diagram shows six different wavelengths (ROYGBV) of incident light approaching the boundary between air and glass.
• The wavelengths form a single ray and were emitted by a single point light source.
• As the ray crosses the boundary between the air and the glass refraction takes place and it bends towards the normal (the dotted green line).
• At the same time, the different wavelengths separate out from one another as dispersion takes place.
• All six wavelengths are refracted towards the normal because they are travelling from air, the faster, less optically dense medium with a smaller refractive index into the glass, a slower, more optically dense medium with the higher refractive index.
• The different paths each wavelength takes in the course of their dispersion results from the fact that the refractive index of the glass is different for each wavelength of light (ROYGBV).

Remember:

• In the right conditions, all transparent media cause incident light to change direction and to disperse into their component colours.
• When light is refracted and changes direction, the angle is determined by the refractive index of the medium it enters.
• Refractive index (n) is equal to the speed of light in a vacuum (c) divided by the speed of light in the medium (v)
• Light travels at 299.792 kilometres per second in a vacuum.
• Only a narrow range of wavelengths that form the full electromagnetic spectrum are visible to the human eye.
• The wavelengths that we can see are known as the visible spectrum.
• The presence of different wavelengths of light around us results in the colours we see in the world.

Refractive index

• The refractive index (also known as the index of refraction) of a transparent medium allows the path of refracted light through a transparent medium to be calculated.
• The refractive index is a ratio calculated by dividing the change in the speed of light in a vacuum by its speed as it travels through a specific medium.
• The refractive index of a medium can be calculated using the formula:

n = refractive index, c = speed of light in a vacuum, v = speed of light in a transparent medium

• When light travels through a vacuum, such as outer space, it travels at its maximum speed of 299,792 kilometres per second.
• When light travels through any other transparent medium it travels more slowly.
• Refractive indices describe the ratio between the speed of light in a vacuum and the speed of light in another medium.
• Most transparent media have a refractive index of between 1.0 and 2.0.
• Whilst the refractive index of a vacuum has the value of 1.0, the refractive index of water is 1.333.
• The ratio between them is therefore 1:1.333
• A simple example of a ratio is of mixing concrete using 1 part of cement to 2 part of sand. The ratio is expressed as 1:2.
• If we divide the refractive index for light travelling through a vacuum (1.0) by the refractive index for glass (1.333) we find that light travels at 75% of the speed of light in a vacuum.

For an explanation of the refractive index (index of refraction) of a medium see: Refractive Index Explained.

For an explanation of how to use the refractive index of a medium see: How to Use the Refractive Index of a Medium.

For an explanation of the Law of Refraction see: Snell’s Law of Refraction Explained.

#### Some key terms

Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the interface between one transparent medium and another.

• As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
• As light passes from a slow medium such as diamond to a faster medium such as glass it bends away from the normal and speeds up.
• In a diagram illustrating optical phenomena like refraction or reflection, the normal is a line drawn at right angles to the boundary between two media.
• A fast (optically rare) medium is one that obstructs light less than a slow medium.
• A slow (optically dense) medium is one that obstructs light more than a fast medium.
• The speed at which light travels through a given medium is expressed by its index of refraction.
• If we want to know in which direction light will bend at the boundary between transparent media we need to know:
• Which is the faster, less optically dense (rare) medium with a smaller refractive index?
• Which is the slower, more optically dense medium with the higher refractive index?
• The amount that refraction causes light to change direction, and its path to bend, is dealt with by Snell’s law.
• Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.

The refractive index of a medium is the amount by which the speed (and wavelength) of electromagnetic radiation (light) is reduced compared with the speed of light in a vacuum.

• Refractive index (or, index of refraction) is a measure of how much slower light travels through any given medium than through a vacuum.
• The concept of refractive index applies to the full electromagnetic spectrum, from gamma-rays to radio waves.
• The refractive index of a medium is a numerical value and is represented by the symbol n.
• Because it is a ratio of the speed of light in a vacuum to the speed of light in a medium there is no unit for refractive index.
• If the speed of light in a vacuum = 1. Then the ratio is 1:1.
• The refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. The ratio is therefore 1:1.333.
• As light undergoes refraction its wavelength changes as its speed changes.
• As light undergoes refraction its frequency remains the same.
• The energy transported by light is not affected by refraction or the refractive index of a medium.
• The colour of refracted light perceived by a human observer does not change during refraction because the frequency of light and the amount of energy transported remain the same.

In the field of optics, dispersion is shorthand for chromatic dispersion which refers to the way that light, under certain conditions, separates into its component wavelengths, enabling the colours corresponding with each wavelength to become visible to a human observer.

• Chromatic dispersion refers to the dispersion of light according to its wavelength or colour.
• Chromatic dispersion is the result of the relationship between wavelength and refractive index.
• When light travels from one medium (such as air) to another (such as glass or water) each wavelength is refracted differently, causing the separation of white light into its constituent colours.
• When light undergoes refraction each wavelength changes direction by a different amount. In the case of white light, the separate wavelengths fan out into distinct bands of colour with red on one side and violet on the other.
• Familiar examples of chromatic dispersion are when white light strikes a prism or raindrops and a rainbow of colours becomes visible to an observer.

ROYGBV is an acronym for the sequence of hues (colours) commonly described as making up a rainbow: red, orange, yellow, green, blue, and violet.

• A rainbow spans the continuous range of spectral colours that make up the visible spectrum.
• The human eye is tuned to the visible spectrum and so to spectral colours between red and violet.
• ROYGBV are colours associated with a range of wavelengths rather than with unique values.
• The visible spectrum is the small band of wavelengths within the electromagnetic spectrum that corresponds with all the different colours we see in the world.
• The fact that we see the distinct bands of colour in a rainbow is an artefact of human colour vision.

In physics and optics, a wave diagram uses a set of drawing conventions and labels to describe the attributes of light waves including wavelength, frequency, amplitude and direction of travel.

• A wave diagram illustrates what happens to a wave as it encounters different media or objects.
• The aim of a wave diagram is to demonstrate optical phenomena such as reflection and refraction.

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation. The measurement is made parallel to the centre-line of the wave.

• The wavelength of an electromagnetic wave is measured in metres.
• Each type of electromagnetic radiation, such as radio waves, visible light and gamma waves,  forms a band of wavelengths on the electromagnetic spectrum.
• The visible part of the electromagnetic spectrum is composed of the range of wavelengths that correspond with all the different colours we see in the world.
• Human beings don’t see wavelengths of visible light, but they do see the spectral colours that correspond with each wavelength and the other colours produced when different wavelengths are combined.
• The wavelength of visible light is measured in nanometres. There are 1,000,000,000 nanometres to a metre.