Prism and Dispersion of Light

Prism and Light Dispersion will help us grasp one of nature’s most beautiful occurrences, the generation of rainbows, which will fascinate you. When sunlight refracts inside a raindrop, it breaks into seven different colours, resulting in a rainbow. The raindrop serves as a prism, dividing the light into its component colours.

Physics is an important and tough subject, it is important for students to learn such important concepts. This way students can score better in the examination. In this article, we will study the concept of Prism and Dispersion of Light in detail.

What is a Prism?

Prism is a transparent medium that can split sunlight into its constituent colours and is bound by three rectangular surfaces and two triangular surfaces.

The rectangular surfaces are inclined to each other and make an angle between them. This angle is the Refracting Angle or Angle of Prism. The rectangular surfaces are the Refracting Surfaces of a Prism. The edge where the two refracting surfaces of a Prism meet is known as the Refracting Edge of the Prism. The cross-section made by the plane perpendicular to the Refracting Edge of the Prism is called the Principal Section of the Prism.

The ray of light passing through a Prism suffers refraction two times and hence deviates through a certain angle from its original path. Let us now study how light refracts through a Prism.

Refraction of Light Through a Prism

Prism and Dispersion of Light can be well understood by studying the Refraction of Light through a Prism. Refraction is the phenomenon of bending the ray of light while entering a medium with a different optical density.

This occurs due to the change in the speed of light in the second medium. Let us now study the path of the ray of light passing through a Prism by considering the below diagram:

Here the ray of light \(\left( {\overrightarrow {PE} } \right)\) is the Incident Ray making an angle with the Normal \(\left( {NN’} \right)\) at the Point of Incidence \(\left( E \right).\) This angle is the Angle of Incidence \(\left( {\angle i} \right).\) Further, the ray of light \(\overrightarrow {PE} \) undergoes refraction at \(E\) and bends towards the Normal \(NN’\) making an angle with the Normal \(NN’.\) This angle is the Angle of Refraction \(\left( {\angle r} \right)\) and the ray \(\left( {\overrightarrow {EF} } \right)\) is the Refracted Ray.

Going ahead, the refracted ray \(\overrightarrow {EF} \) bends away from the Normal \(NN’\) at the point \(F\) and emerges out of the Prism. The ray of light emerging out of the Prism is the Emergent Ray \(\left( {\overrightarrow {FS} } \right)\) that makes an angle with the Normal \(MM’\) at the Point of Emergence \(\left( F \right).\) This angle is the Angle of Emergence \(\left( {\angle e} \right).\)

The sides \(AB\) and \(AC\) as shown in the above diagram, are the Refracting Surfaces of the Prism. These surfaces make an angle with each other that is the Angle of the Prism \(\left( {\angle A} \right).\) Now, if we extend the Incident Ray \(\overrightarrow {PE} \) in the forward direction and the Emergent Ray \(\overrightarrow {FS}\) in the backward direction, then they meet at the point \(G.\) in the backward direction, then they meet at the point \(\overrightarrow {PH}\) gets deviated from its path while passing through the Prism is given by the angle formed between the Incident Ray \(\overrightarrow {PE} \) and the Emergent Ray \(\overrightarrow {FS}.\) This is the Angle of Deviation \(\left( {\angle D} \right).\)

The Angle of Deviation \(\left( {\angle D} \right)\) is related with the Angle of Incidence \(\left( {\angle i} \right),\) the Angle of Emergence \(\left( {\angle e} \right)\) and the Angle of Prism \(\left( {\angle A} \right)\) by the following relation:

\(\angle A + \angle D = \angle i + \angle e\)

Now let us understand the factors on which the Angle of Deviation \(\left( {\angle D} \right)\) depends. They are as mentioned below:

1. The Angle of Incidence \(\left( {\angle i} \right):\) The Angle of Deviation decreases with the increase in the Angle of Incidence to a certain minimum angle called the minimum Angle of Deviation. Later with the increase in the Angle of Incidence, the Angle of Deviation also increases. At the minimum Angle of Deviation, the Angle of Incidence is equal to the Angle of Emergence, and the Angle of Refraction at the first Refracting Surface is equal to the Angle of Refraction at the second Refracting Surface.

2. The Angle of Prism \(\left( {\angle A} \right):\) The Angle of Deviation decreases with the increase in the Angle of Prism.

3. The Refractive Index: The Angle of Deviation increases with the increase in the Refractive Index of the material of Prism.

4. The Wavelength of Light: The Angle of Deviation for the violet light is more than the Angle of Deviation for the red light. Thus, the Angle of Deviation decreases with the increase in the Wavelength of Light. Due to this reason, the lights of different colours travel through different paths and hence splits while passing through a Prism. This phenomenon is known as Dispersion. Let us now understand the concept of Dispersion in detail.

What is Called Dispersion of Light?

Prism and Dispersion of Light are interconnected. A medium like that of a Prism disperses white light into its constituent colours.

Definition of Dispersion: The phenomenon of splitting white light into its constituent colours is known as Dispersion.

The medium that brings about Dispersion is called the dispersive medium. Hence, the Prism that makes white light split into its constituent colours is a dispersive medium.

Cause of Dispersion of Light Through a Prism

Prism does Dispersion of Light because the light of different colours has different wavelengths that are refracted or deviated to different extents. Let us understand the Cause of Dispersion in detail.

Different colours of light of the visible spectrum have different wavelengths or frequencies. The band of colours in the visible spectrum is given by the acronym VIBGYOR (V-Violet, I-Indigo, B-Blue, G-Green, Y-Yellow, O-Orange and R-Red). Among these colours, violet light has the lowest wavelength, and red light has the highest wavelength. Also, violet light has the maximum frequency, whereas red light has the minimum frequency. When white light like Sunlight travels through air or vacuum, all the colours of light travel at the same speed. But when these colours of light enter a dispersive medium like a Prism, their speed changes.

This is because the refractive index of a medium depends on the wavelength of light passing through it. The value of the refractive index of the material of Prism is lesser for the light with a higher wavelength like red than the light with a lower wavelength like violet. So, the material of the Prism is more optically denser for the light of violet colour than for the light of red colour. Hence, the violet coloured light has a lesser speed than the red coloured light. Due to this reason, the violet light bends the most, and the red light bends the least while passing through a Prism.

Now the Refracting Surfaces of the Prism are inclined to each other rather than being parallel to each other. Due to this reason, the light of different colours bend more away from each other, and we see a band of different colours emerge out of a Prism. Thus, the Prism splits the white light into its constituent colours and causes Dispersion.

In other words, the Angle of Deviation for the violet light is more than the Angle of Deviation for the red light. So when white light passes through a Prism, the violet light in it bends the most and appears to emerge out towards the base of the Prism, whereas the red light bends the least and appears to emerge out towards the apex of the Prism as shown in the below diagram:

Recombination of Spectrum of Colours by Prism

Newton experimented on the Recombination of the Spectrum of Colours to form white light. Let us understand this experiment in detail.

Newton passed Sunlight through a Glass Prism and obtained the visible spectrum. Then, he tried to split further the colours obtained from a Glass Prism by using another similar Glass Prism, but he could not get any more colours. So he passed the beam of Sunlight dispersed through a Glass Prism through another identical Glass Prism that was held alongside but in the opposite direction, as shown in the below diagram:

In this arrangement, the first Glass Prism placed on its base disperses the white light or the Sunlight into seven colours. In contrast, the second Glass Prism placed on its apex receives the seven colours of the Sunlight and recombines them into the Sunlight or the white light. Here the Refracting Surfaces of the second Glass Prism are in the opposite direction to the Refracting Surfaces of the First Glass Prism. So, the second Glass Prism is able to recombine the spectrum of colours as the angular Dispersion produced by it is equal and opposite to the angular Dispersion produced by the first Glass Prism.

It is to be noted that the incident white light and the emergent white light may or may not be in the same direction. The inference of this experiment helped Newton conclude that the Sunlight is made up of seven colours. Such a crucial observation forms the basis of our understanding of various natural phenomena occurring in nature. One such natural phenomenon is the Rainbow Formation.

Rainbow Formation Due to Dispersion of Light

Prism and Dispersion of Light are the key concepts that help us to understand the Rainbow Formation. Let us now understand how a Rainbow is formed in nature. Have a look at the breathtaking view of a Rainbow near a waterfall in the below picture:

The Rainbow in the sky is a spectrum of seven colours that occurs in the form of concentric circular arcs when the sun shines on the raindrops during or after a rain shower. The common centre of the concentric circular arcs of the Rainbow lies on the line joining the sun to the eye of the observer.

There are two types of Rainbows: the Primary Rainbow and the Secondary Rainbow. In the above picture, the brighter arc towards the inside is the Primary Rainbow, followed by a dark band and a faint Secondary Rainbow towards the outside. The sequence of colours of a Primary Rainbow is VIBGYOR from the bottom that gets reversed in the case of the Secondary Rainbow.

The tiny water droplets suspended in the air during or after a rain shower, or near a waterfall, or near a water fountain act as a dispersive medium that disperses Sunlight into its seven constituent colours. The essential condition for observing a Rainbow is that the sun must be at the back of the observer’s head. The tiny water droplets suspended in the sky in front of the observer’s eye receives the Sunlight that passes through it and undergoes Dispersion at the first surface. Here the Sunlight splits into its constituent colours and travels further towards the back of the water droplet, where they undergo total internal reflection, due to which their direction changes.

The total internal reflection occurs when a ray of light travels from a denser medium to a rarer medium at an angle more than the critical angle of the denser medium. The critical angle of a medium is the angle of incidence for which the angle of refraction is \(90^\circ; \) that is, the refracted rays goes in a direction perpendicular to the normal at the point of incidence. In other words, the refracted ray just gazes at the refracting surface. For the angle of incidence more than the critical angle of the denser medium, the ray of light, instead of undergoing refraction into the rarer medium, gets reflected into the same denser medium.

Further, the constituent colours of the sunlight, after undergoing total internal reflection at the back of the water droplet, reaches the front side and emerge out of the water droplet towards the observer. Each water droplet suspended in the sky undergo the same phenomena and disperses the Sunlight. The below diagram depicts the path of the Sunlight inside a water droplet:

In the case of a Primary Rainbow, the Sunlight undergoes total internal reflection once and refraction twice before emerging from the water droplet, whereas in the case of a Secondary Rainbow, the Sunlight undergoes total internal reflection twice and refraction twice before emerging out of the water droplet. All the water droplets at an angle of \(42^\circ \) in any direction from the observer contribute to a Primary Rainbow, and all the water droplets at an angle of \(52^\circ \) in any direction from the observer contribute to a Secondary Rainbow.

As any water droplet at a specific angle in any direction contributes to a Rainbow, the Rainbow is a circular arc. A Secondary Rainbow is wider and dimmer than a Primary Rainbow and thus is more difficult to see.

FAQs

Q.1. Which colour deviates the least while passing through a prism?
Ans: The red colour deviates the least while passing through a prism.

Q.2. What is the definition of a prism?
Ans: A prism is a transparent medium bound by three rectangular surfaces and two triangular surfaces.

Q.3. Why does a prism disperse white light but a glass slab don’t?
Ans: The refracting surfaces of a prism are inclined to each other, due to which the incident ray and the emergent ray are not parallel to each other rather have an angle between them called the angle of deviation. The angle of deviation is different for different colours, and so a prism disperses white light. But the refracting surfaces of a glass slab are parallel to each other, due to which the bending of light taking place at the first refracting surface gets reversed when the light further passes through the second refracting surface, and hence there is no dispersion when the light passes through a glass slab.

Q.4. What are the conditions for observing a rainbow?
Ans: For observing a rainbow, there should be a sufficient amount of water droplets suspended in the air like that during or after a rain shower or near a waterfall, and the sun must be at the back of the observer.

Q.5. Which colour deviates the most while passing through a prism?
Ans: The violet colour deviates the most while passing through a prism.

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