Prism Dispersion

Do you know the light that appears to us as white when seen through naked eyes is actually a mixture of seven different colours of light? This was first told by Newton after he performed an experiment with the glass prism.

When he made a ray of white light pass through a glass prism of triangular shape, the white light split into a band of seven different colours on the white screen placed in front of the glass prism. This led to the discovery of the fact that white light is actually a mixture of light of seven different colours. Further, we will study what is dispersion, what is the prism, the reason behind the dispersion of white light, what colours are mixed to form a white light and so on. So let's get started

Dispersion of Light by a Prism

Let’s start with a diagram of light dispersion in a prism, it will help us understand this phenomenon more clearly and precisely.

In the above figure, we can clearly see a beam of white light is passed through a glass prism. On entering the prism the white light splits into a broad patch of seven colours on a screen placed in front of the prism. The splitting up of white light into seven different colours of the ray of light when passed through a prism is called dispersion of light. This clearly shows us that the white light is made up of seven different colours which get separated when this white light is passed through any transparent surface like a glass prism.

Now we should know about the colours that are mixed to form the white light.

White light is incident on a 60°, 60°, 60° prism. Use the slider to change the initial angle of incidence.

You can set the refractive index for red light (n_r) and the difference in indices for red and blue light (n_b-n_r).

The angle of dispersion is the angle between the red and blue rays after they have refracted through the prism.

The angle of deviation is the angle between the line of the incident ray and the final refracted red ray.

Angular Dispersion

Deduction of angular dispersion in thin prism :

The thin prism is always in the position of minimum deviation , It disperses the white light into the seven spectral colours , where :

The angle of deviation of the red light is estimated from the relation :

 ( α_o )_r = A ( n_r – 1 )

The angle of deviation of the blue light is estimated from the relation :

 ( α_o )_b = A ( n_b – 1 )

Where : ( n_r ) is the prism’s refractive index for red light and ( n_b ) is the prism’s refractive index for blue light .

 ( α_o )_b − ( α_o )_r = A ( n_b – n_r )

The value ( α_o )_b − ( α_o )_r is called the angular dispersion between the blue and the red rays.

Factors affect the angular dispersion :

1. The apex angle of the prism .

2. The prism’s refractive index for both blue and red colours .

The Seven Colours

The band of seven colours which is formed on a white screen when a beam of white light is passed through a transparent material like a glass prism is called a spectrum of white light. 

(Image will be uploaded soon)

The Seven Colours in the Band Appearing on the White Screen are:

Red, Orange, Yellow, Green, Blue, Indigo and Violet and these seven colours are together denoted as a term called VIBGYOR where V denotes Violet I denotes Indigo B denotes Blue G denotes Green Y denotes Yellow O denotes Orange and R denotes Red.

So now we know about a lot of things about the dispersion of white light and it's time to know the reason behind the dispersion of white light by a glass prism

Dispersion of White Light by a Glass Prism

The basic reason behind the dispersion of white light into seven different colours is because all the seven rays of light of different colours travel at different speeds through the glass prism. The degree of refraction also can be said as the bending of each light ray depends upon their individual speed while passing through the prism. All the different colours of light ray travel at different speeds in glass and so the angle of bending or angle of refraction of each light ray is different. Out of the seven colours in the spectrum of white light red is the colour which has a maximum speed in the glass prism and hence it's the angle of deviation is the least Because of which red colour forms the upper part of the spectrum. On the other hand, violet is the colour in the spectrum of white light which has minimum speed in the glass prism hence it's the angle of deviation is the most. Because of this Violet colour forms the lowermost part of the spectrum. All seven colours differ in their frequencies. We should know that frequency is inversely proportional to the wavelength. Hence, the order of colours of the spectrum in order of increasing frequencies and decreasing wavelength are Red, Orange, Yellow, Green, Blue, Indigo, Violet. 

The dispersion of white light happens because of the angle of refraction. The process of refraction is defined as the blending of light when it passes from one medium to another medium. The light deviates twice on passing through the glass prism, initially when it enters the prism and the second time when it comes out of it. Since all the colours have different wavelengths and are refracted from different frequencies and deviation angles, hence the Violet colour blends the most and red the least. 

What is a Prism?

A prism is a triangular object made up of glass which is transparent. It has two triangular ends and three rectangular faces or three rectangular sides. The opposite faces of the glass prism are not parallel to each other but are opposite to each other. Also, these opposite faces of a triangular prism are inclined at an angle to one another. The angles between the opposite faces of the glass prism are called the angle of the prism.

Above is the diagram of a prism. This is the real prism but in order to explain the phenomenon of dispersion and for the sake of ease of understanding the glass prism is considered to be a perfect triangle as shown in the figures above while explaining the dispersion of white light and formation of the spectrum.

Type of Dispersion Prisms

Equilateral Dispersion Prism: 60°- 60°- 60°

Isoscele Prism: 30°- 60°- 90°

Littrow Prism: 30°- 60°- 90° with one side HR coating

Pellin-Broca Prism: 90° -75° 135° -60°, features with Brewster angle input and output, and bends light by 90°. It is good for laser beam separation such as SHG, THG.

Ultrafast Laser Dispersion Prism Pair - These Dispersion Prism Pairs are used to compensate for spectral dispersion that occurs in ultrafast laser systems. The prism pairs are matched to within a few arcseconds and are designed so that the input and output angles are both at Brewster's Angle.

Compound Dispersion Prism such as Amici Prism - A compound prism is a set of multiple triangular prism elements placed in contact, and often cemented together to form a solid assembly. 

Rainbow is an Example of Dispersion of Sunlight

After a rain-shower, water droplets suspended in the atmosphere act like tiny prisms for the sunlight. They refract and disperse the incident sunlight, then reflect it internally, and finally refract it again when it comes out of the raindrop. We see the colours in a rainbow because of the dispersion of sunlight inside a raindrop. 

Two essential conditions for a rainbow to form:

• The sun should at the opposite side of the viewing direction,

• Suspended water droplets must be present in the air.

Fun Fact

Dispersion of white light cannot only be seen through making a white light pass through a glass object like a prism. This phenomenon occurs even naturally. Have you ever seen a rainbow? The beautiful rainbow is the best natural example of dispersion of light. The rainbow is an arch of seven different colours visible in the sky produced because of the dispersion of sunlight through the raindrops.