Chromatic Dispersion in a Prism

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In this diagram a ray of incident light strikes one of the three rectangular surfaces at an angle so that it exits from the middle of another.


  • The light source used produces white light which is focused into a narrow beam.
  • As the ray enters the prism the angles of incidence and refraction are the same.
  • When the light exits the prism the angles of incidence and refraction are the same.

Description

Chromatic Dispersion in a Prism

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Yes! Every wavelength of light is affected to a different degree by the refractive index of a transparent medium and as a result, changes direction by a different amount when passing from air to glass or glass to air.
Yes! Light separates into different colours during the course of refraction.
Every wavelength of light is affected to a different degree by the refractive index of a material and as a result changes direction by a different amount when passing from one medium (such as air) to another (such as glass or water).
Chromatic dispersion refers to the way that light separates into its component wavelengths (and so colours), under certain conditions.
It is the small difference in the refractive index of different wavelengths of incident light that causes dispersion and separation of white light into rainbow colours.

About the diagram

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:

Overview

Let’s start off by reviewing what the terms refraction and dispersion refer to and sort out exactly what a prism is.

Refraction

  • When light crosses the boundary between two different transparent media it undergoes refraction.
  • The effect of refraction is that light changes speed and its direction of travel.
  • The change in speed can be calculated if the refractive index is known.
  • The index of refraction can be calculated if the speed of light in a vacuum and the speed of light in the medium is known.
  • The refractive index of a medium is calculated using the formula: Where n = refractive index, c = speed of light in a vacuum, v = speed of light in a transparent medium.
  • The amount that the path of a ray of light bends when it changes direction is calculated using the Law of refraction (also known as Snell’s law).

Chromatic dispersion

Chromatic dispersion is often simply called dispersion.

  • Whenever you see a rainbow of colours in a patch of oil, in the edge of a sheet of glass or a crystal, it is caused by dispersion.
  • White light, containing all wavelengths of the visible spectrum, disperses into a rainbow of colours.
  • Dispersion takes place because the refractive index of any transparent medium is different for each wavelength of light.
  • The diagram at the top of the page shows that in certain circumstances when white light strikes a prism, a rainbow of colours become visible to an observer.

Prism

In the field of optics, a prism is made of glass or other transparent material with flat, polished surfaces.

  • Prisms are generally made from crown or flint glass depending on their intended use.
  • Flint glass prisms are often used for experimental purposes to study the refraction and dispersion of light.
  • A triangular prism consists of two triangular ends and three rectangular faces.
  • If white light is to be refracted or dispersed by a prism into its component colours a narrow beam is pointed towards one of the rectangular faces.
    • Dispersive prisms are used to break up light into its constituent spectral colours.
    • Reflective prisms are used to reflect light, in order to flip or invert a light beam.
  • Triangular reflective prisms are a common component of cameras, binoculars and microscopes.

Crown glass

Crown glass is a type of optical glass made without lead or iron and used in the manufacture of lenses and other tools and equipment concerned with the visible part of the electromagnetic spectrum.

  • Crown glass produces low levels of chromatic dispersion which is of particular concern in the manufacture of lenses.
  • Dispersion is unavoidable but a well-designed lens is able to reorganize light so that, in the end, all wavelengths converge at the same point and so produce a sharp image with a high degree of colour accuracy.

Flint glass

Flint glass is made from a combination of silicon dioxide (SiO2) and lead or potassium.

  • Flint glass typically has a higher refractive index value than crown glass which means that dispersion is more evident.
  • Flint glass absorbs most ultraviolet light but comparatively little visible light and is often used in telescope lenses.

The diagram

In this diagram a ray of incident light strikes one of the three rectangular surfaces at an angle so that it exits from the middle of another.

  • The light source used produces white light which is focused into a narrow beam.
  • As the ray enters the prism the angles of incidence and refraction are the same.
  • When the light exits the prism the angles of incidence and refraction are the same.
  • The light source and prism are arranged on a suitable surface, such as a piece of paper so that the dispersed colours are visible to an observer.
  • Remember that light is only visible when either its source is in view or when transmitted light strikes a surface, in this case, the paper.
  • The human eye sees white when all the colours that make up visible light are combined together and strike a neutral coloured surface that reflects all wavelengths equally.

Remember that:

  • The incident white light is refracted towards the normal as it enters the prism because the optic density of glass is greater than air.
  • On entry to the prism, a small amount of dispersion takes place.
  • As the dispersed colours exit the prism they are refracted away from the normal because the optic density of air is less than air.
  • On exiting the prism, the amount of dispersion of each colour is more pronounced.
  • The amount that light bends as refraction and dispersion take place depends on:
    • The type of glass.
    • The composition of wavelengths produced by the light source.
    • The angle of incidence of the light.
    • The refractive index of the glass for each wavelength.

Some key terms

A light source is a natural or man-made object that emits one or more wavelengths of light.

  • The Sun is the most important light source in our lives and emits every wavelength of light in the visible spectrum.
  • Celestial sources of light include other stars, comets and meteors.
  • Other natural sources of light include lightning, volcanoes and forest fires.
  • There are also bio-luminescent light sources including some species of fish and insects as well as types of bacteria and algae.
  • Man-made light sources of the most simple type include natural tars and resins, wax candles, lamps that burn oil, fats or paraffin and gas lamps.
  • Modern man-made light sources include tungsten light sources. These are a type of incandescent source which means they radiate light when electricity is used to heat a filament inside a glass bulb.
  • Halogen bulbs are more efficient and long-lasting versions of incandescent tungsten lamps and produce a very uniform bright light throughout the bulb’s lifetime.
  • Fluorescent lights are non-incandescent sources of light. They generally work by passing electricity through a glass tube of gas such as mercury, neon, argon or xenon instead of a filament. These lamps are very efficient at emitting visible light, produce less waste heat, and typically last much longer than incandescent lamps.
  • An LED (Light Emitting Diode) is an electroluminescent light source. It produces light by passing an electrical charge across the junction of a semiconductor.
  • Made-made lights can emit a single wavelength, bands of wavelengths or combinations of wavelengths.
  • An LED light typically emits a single colour of light which is composed of a very narrow range of wavelengths.

In physics and optics, a medium refers to any material through which light or other electromagnetic waves can travel. It’s essentially a substance that acts as a carrier for these waves.

  • Light is a form of electromagnetic radiation, which travels in the form of waves. These waves consist of oscillating electric and magnetic fields.
  • The properties of the medium, such as its density and composition, influence how light propagates through it.
  • Different mediums can affect the speed, direction, and behaviour of light waves. For instance, light travels slower in water compared to a vacuum.
  • Examples of Mediums:
    • Transparent: Materials like air, glass, and water allow most light to pass through, with minimal absorption or scattering. These are good examples of mediums for light propagation.
    • Translucent: Some materials, like frosted glass or thin paper, partially transmit light. They allow some light to pass through while diffusing or scattering the rest.
    • Opaque: Materials like wood or metal block light completely. They don’t allow any light to travel through them.

Wavelength measures a complete wave cycle, which is the distance from any point on a wave to the corresponding point on the next wave.

  • While wavelength can be measured from any point on a wave, it is often simplest to measure from the peak of one wave to the peak of the next or from the bottom of one trough to the bottom of the next, ensuring the measurement covers the whole of the cycle.
  • The wavelength of an electromagnetic wave is usually given in metres.
  • The wavelength of visible light is typically measured in nanometres, with 1,000,000,000 nanometres making up a metre.
  • Radio waves, visible light, and gamma waves for example, each have different ranges of wavelengths within the electromagnetic spectrum.

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.

  • The angle of refraction is measured between a ray of light and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • See this diagram for an explanation: Refraction of a ray of light
  • If the boundary between the media is curved, the normal is drawn perpendicular to the boundary.

A colour model is a system or framework used to understand, organise, and manipulate colour. It ranges from basic concepts, such as the sequence of colours in a rainbow, to more advanced models like RGB, CMYK, and CIE, which are essential for accurate colour reproduction in various fields, including digital media, printing, and manufacturing.

  • A colour model, underpinned by colour theory, provides a precise and replicable approach to understanding:
    • How the human eye perceives light and interprets colour.
    • Different types of colour, including those produced by mixing lights, pigments, or inks.
    • How to manage the diverse ways colour is processed by devices such as cameras, digital screens, and printers.
  • Colour models enable us to:
    • Make sense of colour in relation to human vision and the world around us.
    • Use colours in logical, predictable, and replicable ways.
    • Understand how to mix specific colours, whether using lights, pigments, inks, or dyes.
    • Specify colours using names, codes, notations, or equations.
    • Organise and apply colour for different purposes, from fabrics and interiors to vehicles.

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

  • Light bends towards the normal and slows down when it moves from a fast medium (like air) to a slower medium (like water).
  • Light bends away from the normal and speeds up when it moves from a slow medium (like diamond) to a faster medium (like glass).
  • These phenomena are governed by Snell’s law, which describes the relationship between the angles of incidence and refraction.
  • The refractive index (index of refraction) of a medium indicates how much the speed and direction of light are altered when travelling in or out of a medium.
  • It is calculated by dividing the speed of light in a vacuum by the speed of light in the material.
  • Snell’s law relates the angles of incidence and refraction to the refractive indices of the two media involved.
  • Snell’s law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices.

As light crosses the boundary between two transparent media, the law of refraction (Snell’s law) states the relationship between the angle of incidence and angle of refraction of the light with reference to the refractive indices of both media as follows:

When electromagnetic radiation (light) of a specific frequency crosses the interface of any given pair of media, the ratio of the sines of the angles of incidence and the sines of the angles of refraction is a constant in every case.

  • Snell’s law deals with the fact that for an incident ray approaching the boundary of two media, the sine of the angle of incidence multiplied by the index of refraction of the first medium is equal to the sine of the angle of refraction multiplied by the index of refraction of the second medium.
  • Snell’s law deals with the fact that the sine of the angle of incidence to the sine of the angle of refraction is constant when a light ray passes across the boundary from one medium to another.
  • Snell’s law can be used to calculate the angle of incidence or refraction associated with the use of lenses, prisms and other everyday materials.
  • When using Snell’s law:
    • The angles of incidence and refraction are measured between the direction of a ray of light and the normal – where the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
    • The wavelength of the incident light is accounted for.
    • The refractive indices used are selected for the pair of media concerned.
    • The speed of light is expressed in metres per second (m/s).

Visible light refers to the range of wavelengths of electromagnetic radiation that is perceived as colour by human observers. While the range of visible light is generally considered to be 400-700 nm, the exact range of colours perceptible can vary slightly between individuals.

  • Visible light is one form of electromagnetic radiation. Other forms of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. Visible light ranges from approximately 400 nanometres (nm) for violet to 700 nm for red.
  • A human observer perceives visible light as a combination of all the spectral colours between red and violet, as well as a vast range of other colours produced from the blending of different wavelengths in varying proportions.

Rainbow colours are the colours seen in rainbows and in other situations where visible light separates into its different wavelengths and the spectral colours corresponding with each wavelength become visible to the human eye.

  • The rainbow colours (ROYGBV) in order of wavelength are red (longest wavelength), orange, yellow, green, blue and violet (shortest wavelength).
  •  It is the sensitivity of the human eye to this small part of the electromagnetic spectrum that results in our perception of colour.
  • The names of rainbow colours are a matter more closely related to the relationship between perception and language than anything to do with physics or scientific accuracy. While the spectrum of light and the colours we see are both determined by wavelength, it’s our eyes and brains that turn these differences in light into the colours we experience.
  • In the past, rainbows were sometimes portrayed as having seven colours: red, orange, yellow, green, blue, indigo and violet.
  • Modern portrayals of rainbows reduce the number of colours to six spectral colours, ROYGBV.
  • In reality, the colours of a rainbow form a continuous spectrum and there are no clear boundaries between one colour and the next.

 

 

Optical density is a measure of how much a material resists and slows the transmission of light.

  • The higher the optical density of a material, the slower light travels through it.
  • The lower the optical density of a material, the faster light travels through it.
  • A vacuum is not a medium and has zero optical density.
  • Light travels through a vacuum at the maximum possible speed of light which is 299,792 kilometres per second.
  • Optical density and refractive index are related properties.
  • In general, materials with higher optical density tend to have higher refractive indices and vice versa.
  • The greater the difference in refractive index between two materials, the more they will bend light when they come into contact.

 

 

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