Dispersion of light and formation of Rainbow

 

DISPERSION:

The splitting of white light into different colours (VIBGYOR) is called

Dispersion.

When a white light is sent through a prism with some angle with the surface, it splits into seven different colours.

  We can consider that white light is a collection of waves with different wavelengths. Violet colour is known to have the shortest wavelength while red is of the longest wavelength.

 

  According to wave theory, light can be thought of a wave propagating in all directions. Light is an electromagnetic wave. Here no particle physically oscillates back and forth. Instead, the magnitude of electric and magnetic fields, associated with the electromagnetic wave, vary periodically at every point. These oscillating electric and magnetic fields propagate in all directions with the speed of light.

 The reason lies in the fact that, while the speed of light is constant in vacuum for all colours, it depends on the wavelength of light when it passes through a medium.

 The refractive index of a medium depends on wavelength of light. When white light passes through a medium, each colour selects its least time path and we have refraction of different colours to different extents. This results in separation of colours, producing a spectrum.

  Refractive index decreases with an increase in wavelength. If we compare the wave lengths of seven colours in VIBGYOR, red colour has longest wavelength and violet colour has shortest wavelength. The refractive index of red is low hence it suffers low deviation.

     We know that the frequency of light is the property of the source and it is equal to number of waves leaving the source per second. This cannot be changed by any medium. Hence frequency doesn’t change due to refraction. Thus coloured light passing through any transparent medium retains its colour.

     While refraction occurs at the interface, the number of waves that are incident on the interface in a second must be equal to the number of waves passing through any point taken in another medium. This means that the frequency of the light wave remains unaltered while its wavelength changes depending on the medium through which it passes. We know that the relation between the speed of wave (v), wavelength ( λ) and frequency (f) is

v = f λ (frequency (f) may be denoted by υ)

For refraction at any interface, v is proportional to λ. Speed of the wave increases with increase in wavelength of light and vice versa.

 

FORMATION OF RAINBOW:

 This is a good example of dispersion of light observed in nature.

The beautiful colours of the rainbow are due to dispersion of the sunlight by millions of tiny water droplets. Let us consider the case of an individual water drop.

Observe figure above. The rays of sunlight enter the drop near its top surface. At this first refraction, the white light is dispersed into its spectrum of colours, violet being deviated the most and red the least. Reaching the opposite side of the drop, each colour is reflected back into the drop because of total internal reflection. Arriving at the surface of the drop, each colour is again refracted into air. At the second refraction the angle between red and violet rays further increases when compared to the angle between those at first refraction.

 The angle between the incoming and outgoing rays can be anything between 00 and about 42⁰. We observe bright rainbow when the angle between incoming and outgoing rays is near the maximum angle of 42⁰. Although each drop disperses a full spectrum of colours, an observer is in a position to see only a single colour from any one drop depending upon its position.

If violet light from a single drop reaches the eye of an observer, red light from the same drop can’t reach his eye. It goes elsewhere possibly downwards of the eye of the observer. To see red light, one must look at the drop higher in the sky. The colour red will be seen when the angle between a beam of sunlight and light sent back by a drop is 42⁰. The colour violet is seen when the angle between a sunbeam and light sent back by a drop is 40⁰. If you look at an angle between 40⁰ and 42⁰, you will observe the remaining colours of VIBGYOR.

A rainbow is not the flat two dimensional arc as it appears to us. The rainbow you see is actually a three dimensional cone with the tip at your eye as shown in figure.  All the drops that disperse the light towards you lie in the shape of the cone – a cone of different layers. The drops that disperse red colour to your eye are on the outer most layer of the cone, similarly the drops that disperse orange colour to your eye are on the layer of the cone beneath the red colour cone. In this way the cone responsible for yellow lies beneath orange and so on it till the violet colour cone becomes the innermost cone.

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