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Chapter 4 – Dispersion Of White Light By a Glass Prism

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Have you ever seen a beautiful rainbow in the clear sky after a rainy day? Or a colourful glow caused by the sunlight’s falling onto a piece of glass? The great scientist Issac Newton was barely 13 years old that ignited his curiosity to research extensively for the theory of ‘light and colours’. On 19 February 1672, he documented in his book Philosophical Transactions, as it led to the field of ‘Ray Optics’ and that is what we know and study till date. 

Visible light is known to display dual nature. Under some conditions, it travels in a straight line like a particle, and otherwise, it propagates in the form of a wave. Prism, a transparent optical element has been observed to display a phenomenon called dispersion of light.

  • When light is incident on to the plane of the surface of a glass prism, it is ‘dispersed’ as it gets split into separate components, having their constituent colours. The universal pattern that is followed by these colour components of light makes up the spectrum of visible light. 
  • VIBGYOR is the pattern that makes up a rainbow, and when sunlight or white light is passed through a glass prism. 
  • Sir Isaac Newton’s insightful yet straightforward experiment of dispersing the sunlight into its component colours, and then holding an upside-down that uses the dispersed wave of colourful light as an incident (input) ray. This resulted in a ray of white light that perfectly resembled the sunlight that was used as an incident ray for the first prism.
  • Formula: Prism of angle A, having refractive index n2, placed on a medium of refractive index n1 follows the formula –
  • n_{21} = \frac{n_2}{n_1} = \frac{ sin[A+D_m]/2 }{sin(A/2)}, with Dm as the angle of minimum deviation
  • Dispersion of light essentially occurs when an optical device like a prism, is placed in front of a ray of white light (sunlight), the ray gets dispersed. Violet, indigo, blue, green, yellow, orange, and red, are the colours that are observed to combine to form visible light. 
  • Violet light has a 400nm wavelength and has a frequency of 7.5 *, while red light has a wavelength of 700 nm and a frequency of 4.3 * 1014. 
  • This causes them to display unique characteristics, and travel at different speeds through the prism. The difference in their respective frequencies causes these infinitesimal differences in their speeds.
  • Example 1: A rainbow is a prime example of dispersion of white light by water droplets that act as a prism to disperse the light into colour components.
  • Example 2: Dispersion Of White Light By A Glass Prism is a primary and fundamental example for the phenomenon of dispersion of light.
  • Light, even in its dual nature, tends to move in a straight line through a medium. But when the light travels from mediums, the relative difference in the densities of those mediums affects the path followed by the light.
  •  Density difference affects the refractive index of those particular mediums’ interface. When visible light and/or Electro-Magnetic radiation travels through our atmosphere, the density of air changes as we move from the surface to the ionosphere. 
  • Thus solar flares, UV light, and even the twinkling of stars can be observed to deviate from its intended straight path. This phenomenon is known as the atmospheric refraction of light.
  • For example, Astronomical refraction (twinkling) is the refraction caused by the turbulence present in the Earth’s atmosphere that causes stars to fluctuate their appearance from bright to faint.
  • Formula: Snell’s Law
    n_1sin\theta_1 = n_2sin\theta_2
    Where n1 is an incident index, n2 is the refractive index, \theta_1 is an incident angle, \theta_2 is the refracted angle.
  • Light has its velocity and frequency at which it travels, as it also has its wavelength. The constituent colours have their properties, as they vary based on their sequence in the spectrum. The light with shorter wavelengths gets scattered to an increased extent, as compared to light with longer wavelengths. 
  • The dust, moisture, and other tiny particles present in the atmosphere cause’ scattering of light‘, which is the primary cause for the difference in the colour of the sun during dusk and dawn.
  • The total atmospheric distance that sunlight needs to travel, before reaching our eyes, scatters the violet light that has low wavelengths, thus only allowing orange and red shades of sunlight. Rayleigh scattering gives the sky its inherent blue colour.
  • The law states that the amount of scattering observed is inversely proportional to the fourth power of the wavelength. (~λ−4)
  • Formula: Assuming that R is the amount of scattering, the equation is: R 14
  • For example, The true colour of the sun is white, and the space is black when viewed from a point outside the Earth’s atmosphere. But the atmospheric particles scatter the light giving blue colour to the sky and a yellow shade to the sun.
  • Tyndall Effect is observed when a beam of light is placed upon a colloid, or a superfine suspension, scattering of light by particles is observed that is commonly known as ‘Tyndall Scattering’. 
  • When light is placed upon a solution such as water, almost no scattering is observed, while a colloid such as milk gives out visible scattering. Suspensions with particulate matter emphasise the scattering, making it more evident and visible. Longer wavelengths transmit themselves effectively, while shorter wavelengths tend to be more diffusely reflected in Tyndall effect. 
  • Presence of 40-900 nm particles in the suspension can cause this phenomenon, as they are approximately close to the wavelengths of visible light.
  • For example, The path followed by sunlight entering a dark room is visible, often highlighted by dust particles that shine in it, is an example of Tyndall Effect.
  • Sunlight, when dispersed through a glass prism, is split up into 7 colours, and it can be combined to form the same monochromatic white light that resembles sunlight. This recombination is observed due to the same properties of prism that is placed upside down in front of the 1st prism, in a way that light dispersed from the first prism is placed as an incident light onto the 2nd inverted (upside down) prism. 
  • This recombination of the spectrum of colours has helped the scientists to conclude that the visible light is made up of 7 components of colours, in a simple yet effective manner.
  • For example, Spectrum of colours of sunlight that gets separated by a prism recombines with an inverted prism as below:

The concept of dispersion of white light by a glass prism is one of the most fundamental concepts within the topic of Ray Optics. Such concepts, when taught and explained through audio-visual means, combined with real-life examples, can make them easier to grasp for students.

1. How does the dispersion of white light take place when it passes through a glass prism?

White light is made up of constituent colours of light that have their unique refractive indices. Their difference in wavelength causes them to have different angles of deviation, which is made up of colours with red light bending the least and violet light bends the most.

 

2. Why is light dispersed by a glass prism?

 

The light that falls upon the surface of the prism gets separated into lights of component colours, which is called as Dispersion Of White Light By A Glass Prism. The colours have different wavelengths that travel at velocities through the transparent prism. This causes light to disperse by a glass prism due to the difference in the medium of propagation.

3. What is meant by the dispersion of white light? Draw a neat diagram to show the dispersion of white light by a glass prism. What is the cause of dispersion?

White light or sunlight gets dispersed into 7 component colours, VIBGYOR, with violet bending the most, and red bending the least. The separation of white light into component colours is known as the dispersion of light.

The cause for dispersion is that violet has a shorter wavelength, which slows it down more, compared to red light with a longer wavelength that is the least dispersed.

4. What is the dispersion of white light? State its cause?

Dispersion of white light is an optical phenomenon, wherein sunlight/white light that is incident upon glass prism is split into its constituent colours, namely VIBGYOR. A dispersive glass prism causes this phenomenon due to its refractive index varying with the wavelengths of the individual colours that combine to form the sunlight. Refractive Index (I) variation causes a change in the resultant angle of deviation, thus causing the sunlight to be split spatially, giving out the spectrum of colours.

5. What is the reason for dispersion?

Light in itself has specific characteristics to it. As it travels through the medium, it possesses a certain wavelength, and it tends to travel in a straight line. Following the Snell’s Law that defines the formula for angles and their indexes, we can infer that the dispersion is caused due to the nature of the dispersive optical device (Prism) that has a different refractive index than air, the previous medium of propagation. This difference in the refractive index causes the light having constituent colours of different wavelengths, to be bent at different angles, thus splitting them into those colours spatially.

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