Chromatic Dispersion in a Prism

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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:

• Introducing reflection
• Types of reflection
• Introducing refraction
• Calculating the angle of refraction
• Introducing chromatic dispersion
• Introducing refraction and wavelength

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.