# Dispersion of Light

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12.5Dispersion of Light

In this Physics tutorial, you will learn:

• What is dispersion of light?
• Which light colour experiences dispersion?
• Why does light experience dispersion?
• What is an example of natural dispersion of light?
• What are the primary colours of light?
• What light colours are considered as secondary and tertiary?
• How do we use prisms to produce dispersion of light?

## Introduction to Dispersion of Light

Have you ever seen a rainbow in the sky? When does it occur? Why?

Which light do you think includes all colours? Explain.

How can you split the white light into colours?

Have you ever heard the term "dispersion"? What does it mean?

Try to answer the above questions but do not consider this as an obligation. It is OK even if you don't known the answers. You will have chance to know them by the end of this tutorial.

## Recap of Visible Light and Its Colours

In the Physics tutorial on the Features of Light, it was explained that visible light is a small part of EM spectrum ranging in wavelength from 400 nm to 700 nm or from 0.42 THz to 0.75 THz in frequencies (T stands for Tera = 1012). The weakest part of visible light is the red light while the violet light is the most powerful. This means energy of light waves is proportional to their frequency and inversely proportional to the wavelength.

The order of colours from the weakest to the strongest is shown below.

Red → Orange → Yellow → Green → Cyan → Blue → Violet

Or There are no fixed border between colours. However, a rough estimation gives the following values for the wavelengths of the above colours of light.

Red → 700 nm - 635 nm

Orange → 635 nm - 590 nm

Yellow → 590 nm - 560 nm

Green → 560 nm - 520 nm

Cyan → 520 nm - 490 nm

Blue → 490 nm - 450 nm

Violet → 450 nm - 400 nm

## The Meaning of Dispersion

Light produced by the Sun is normally white. When the white light passes through other transparent media, it refracts. As a result, it changes its original direction. The amount of refraction is determined by the angle of incidence, as explained in the Physics tutorial covering the Refraction of Light.

If the thickness of the refractive medium is constant, the white light will remain white during and after refraction as shown in the figure. This is because all parts of the white light beam experience the same amount of refraction when passing through the second medium.

On the other hand, when the same white light beam falls on a refractive transparent medium with non-constant thickness, it will split into colours because they are incident at different angles and as a result, not all parts of the original beam travel the same distance through the refractive medium. Hence, the light waves of this beam will experience a deviation in proportion to the path they travel inside the refractive medium as shown in the figure below. The phenomenon observed in the above figure is known as "dispersion of light". By definition:

The phenomenon of splitting of visible light into its component colours is called dispersion.

Dispersion of light is caused by the change of speed of light ray resulting in a different angle of deviation for each wavelength.

We can observe dispersion in natural form when seeing the rainbow after rain. This phenomenon occurs because immediately after raining, the air still contains a large number of small droplets of water, which act as tiny prisms. Therefore, they cause the dispersion of sunlight into component colours as shown in the figure below. We cannot observe any dispersion when using monochromatic (one colour) light because only white light contains all colours. A monochromatic light ray (for example a light ray produced by a laser) will simply refract when passing through prisms without causing any dispersion. If the dispersed rays enter in another prism placed in the opposite direction as the original prism, a white light ray is produced, i.e. the reverse process of dispersion does occur as shown in the figure below. ## Primary, Secondary and Tertiary Colours of Light

Although we see seven colours when white light disperses through prisms, only three of them are primary, i.e. are not produced by combinations of other colours. These primary colours are red, green and blue. Indeed, we hardly see all seven colours during dispersion because the three primary colours are more visible than the others.

On the other hand, three other colours known as secondary colours are obtained by combining two primary colours. They are magenta, cyan and yellow. Thus, magenta is obtained by combining red and blue, cyan by combining green and blue, and yellow light is obtained by combining red and green. Look at the figure below. The other colours not mentioned in the above categories, are obtained by combining one primary and one secondary colour of light. These colours are known as tertiary or intermediate. For example, if you mix cyan and blue you obtain a new colour known as azure, by mixing blue and magenta you obtain violet etc. There are also quaternary and quinary colours obtained by mixing two tertiary and quaternary colours respectively. However, we will stop here with colours as this is not an advanced tutorial aiming to explain in detail the colours of light but simply a generic tutorial on dispersion of light waves.

Remark! In the Theory of Light, red, blue and green are the primary colours. However, in Painting Theory used in art, the three primary colours are red, yellow and blue. As a result, the secondary and tertiary colours in art are a little different to those in optics. This may cause a bit confusion when doing a research in internet. Hence, it is important to specify the field when you are browsing online for colours.

### Example 1

A student is trying to find a relationship between colours and he chooses the wavelength as criterion to consider when working to prove his assumption. The student claims that secondary colours are obtained when mixing two primary colours in equal amount. Is his assumption correct? Explain.

### Solution 1

From the table below showing the wavelengths of the (seven) rainbow's colours

Red → 700 nm - 635 nm

Orange → 635 nm - 590 nm

Yellow → 590 nm - 560 nm

Green → 560 nm - 520 nm

Cyan → 520 nm - 490 nm

Blue → 490 nm - 450 nm

Violet → 450 nm - 400 nm

we obtain the following typical values for the three primary colours, red, green and blue (typical values are taken near the middle of each wavelength range. Thus, for red colour, we take 670 nm, for green 540 nm and for blue 470 nm as typical wavelengths.

By combining blue and green in equal amounts (based on the student's assumption), we obtain

unknown wavelength (supposedly cyan) = blue wavelength + green wavelength/2
= 470 nm + 540 nm/2
= 505 nm

This wavelength belongs to cyan colour as supposed.

On the other hand, when mixing red and blue in equal amounts, we obtain

unknown wavelength (supposedly magenta) = blue wavelength + red wavelength/2
= 470 nm + 670 nm/2
= 570 nm

This colour belongs to the yellow part of visible light spectrum, not magenta.

Finally, when mixing red and green light in equal amounts, we obtain

unknown wavelength (supposedly yellow) = red wavelength+green wavelength/2
= 670 nm+540 nm/2
= 605 nm

This wavelength belongs to orange part of visible light spectrum, not yellow. Therefore, the student's assumption is not correct, as the colours obtained during the colours mixing process in equal amount do not correspond to the expected colours.

## Totally Reflecting Prisms

Glass prisms can be used to change the direction of light. Right-angled prisms (with angles 45°-45°-90°) and equilateral prisms (with all angles equal to 60° for each corner) are the most common types of prisms and are shown in the figure below. The light ray entering the glass prism cannot pass into air from the long side of the prism as seen in figure below. This is because the light ray strikes this surface at an angle of incidence of 45° which is greater than the critical angle for glass (41.8°). Thus, total reflection occurs inside the glass (remember the phenomenon of total internal reflection explained in our Physics tutorial on the Refraction of Light). Thus, at the end of process the direction of light changes by 90°. ### Example 2

What is the path of the refracted light rays for the incident rays shown in the figure? Prisms are identical and their adjacent bases are in parallel with each other. ### Solution 2

We know that if the angle of incidence for glass is greater than 41.80, the light cannot pass into air, and so, the total internal reflection occurs inside the prism. This phenomenon occurs in both situations shown in the figure. Therefore, the rays follow the paths shown below. ## Whats next?

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