How to Use Refractive Indices

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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 of this page

• This page explains how to use the refractive index of a medium (also called the index of refraction).
  
• Related terms, including reflection, refraction and chromatic dispersion are covered on earlier pages of this series.
• Introductions to the terms refractive index and the law of refraction (sometimes called Snell’s law) also appear 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 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.

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

An overview of 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.

Optical density

The speed at which light travels depends on the medium it is passing through because the optical density of every type of transparent media is different. The result is refraction.

Optical density is a measurement of the degree to which a medium slows the transmission of light:

• The more optically dense a material, the slower light travels.
• The less optically dense a material, the faster light travels.
• A vacuum has the lowest optical density of all.
• Diamonds have a very high optical density.

The diagram

• The refractive index of a medium (sometimes called the index of refraction) is used to calculate the change in speed or direction as light travels from one transparent medium into another.
• The diagram shows an example of how to deduce the speed of a ray of yellow light as it travels through crown glass when its refractive index is known. A table of refractive indices corrected to the wavelength of the ray is shown.
• The equation can be applied to any situation where the optical properties of a specific transparent medium are being investigated.
• Refractive indices are used in the design, manufacture and use of prisms, lenses, optical tools and optical equipment of all types.
• The equation in the diagram demonstrates the direct relationship between the speed of light as it travels through a vacuum (c), the speed of light as it travels through any other transparent medium (v) and the refractive index of a medium (n).
• Because the speed of light in a vacuum is always the same, the formula can be used to calculate:
  • The refractive index (n) of a medium if the speed of light through the medium (v) is known.
  • The speed of light in a medium (v) if its refractive index (n) is known.
• The refractive index of a material (n) can also be used to predict the change of direction of a light ray as it crosses the boundary between transparent media (see Snell’s law of refraction).
• The diagram identifies the symbols commonly used for refractive index (n), speed of light in a vacuum (c) and speed of light of a medium (v).

Remember:

• The speed of light in a vacuum is always 299,792 kilometres per second.
• A vacuum is an empty space, and because there is nothing to obstruct it, light travels through it at its maximum speed.
• The speed of light in any other medium is less than 299,792 km/sec.

• In the right conditions, 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.
• 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.

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

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

Using the diagram

This diagram is in four parts:

• At the top is a definition of the refractive index of a medium which is then shown in the form of an equation.
• Below that is an example of a calculation using the refractive index of a yellow ray of light travelling from air to crown glass.
• A table of refractive indices for a range of different gases, liquids and solids is shown.
• At the bottom is an explanation of the table.

Let’s look at the equation in detail. As the diagram explains, the definition for the index of refraction can be represented in the form of an equation where:

• n = the refractive index of a medium
• c = the speed of light in a vacuum
• v = the speed of light in the medium.

So the equation looks like this:

Now imagine if light were to travel for any distance through a vacuum and then to continue through the vacuum, this would mean that c and v would both be  299,792 kilometres per second (the speed of light in a vacuum) and the index of refraction n = 1. For any other medium, the refractive index is always more than n = 1.

Now, in the example shown in the diagram, a ray of yellow light travels from air into crown glass. The diagram demonstrates how to use a table containing indices of refraction for various different transparent media to find the correct speed of light for the crown glass.
The four steps are shown as follows.

Using the table shown in the diagram the refractive index for crown glass is 1.52. When these values are inserted into the equation it looks like this:

The equation can then be rearranged as follows to find the value for the speed of light v:

By dividing 299,792 by 1.52 we find the speed of light through the crown glass is:

As the note at the bottom of the diagram explains, the refractive indices shown in the table are correct for gasses at 0⁰C and at sea level (where atmospheric pressure =1) and for liquids at 20⁰C.