Define Dispersion: Dispersion of light through Prism, its causes and Dispersive Power

Mar 19 2024

What is Dispersion

Dispersion is the basis for the prism and its ability to separate light according to wavelength. When a light ray passes through a prism it splits up in to its constituent colors producing spectrum of seven colors namely violet, indigo, blue, green, yellow, orange, red. This phenomenon of splitting up of light in two constituent colors is called dispersion. Dispersion is the basis for the prism and its ability to spatially separate light according to wavelength, as illustrated in the following animation.

Dispersion of a White Light by a Glass Prism

The phenomenon of splitting of white light into its seven constituent colours when it passes through a glass prism is called dispersion of white light. The various colours seen are Violet, Indigo, Blue, Green, Yellow, Orange and Red. The sequence of colours remembers as VIBGYOR. The band of seven colours is called the spectrum. The different component colour of light bends at a different angle with respect to the incident angle. The violet light bends the least while the Red bends the most.

Recombination of white light:

Newton found that when an inverted prism is placed in the path of dispersed light then after passing through the prism, they recombine to form white light.

Issac Newton: He was the first, who obtained spectrum of sunlight by using glass prism. He tried to split the spectrum of white light more by using another similar prism, but he could not get any more colours.

He repeated the experiment using second prism in inverted position with respect to the first prism. It allowed all the colours of spectrum to pass through second prism. He found white light emerges on the other side of second prism.

He concluded that Sun is made up of seven visible colours VIBGYOR

Formation of the Rainbow

Rainbow: It is the spectrum of sunlight in nature. It is formed due to the dispersion of sunlight by the tiny water droplet, present in the atmosphere.

The most common dispersion is a rainbow. Sunlight falls on a falling raindrop, the ray is refracted into the drop, and some of the light reflects off the inner surface of the drop and then refracts outward. The first refraction causes the light to split into a spectrum. The second quarry enlarges. Light is refracted in large numbers. Red comes from drops
above and purple below. If the Sun is higher above the horizon, the rainbow cannot be seen.

Formation of the rainbow: The water droplets act like small prism. They refract and disperse the incident sunlight, then reflect it internally, and finally refract it again when it comes out of the raindrop. Due to the dispersion of light and internal reflection, different colours reach the observer’s eye.
Red colour appears on top and violet at the bottom of rainbow.
A rainbow is always formed in a direction opposite to that of Sun.

At ‘A’ – Refraction and dispersion take place.
At ‘B’ – Internal reflection takes place.
At ‘C’ – Refraction and dispersion take place.

Causes of dispersion of light

Different color of light is due to different wavelengths.
Wavelength of violet is smaller than that of red light.
Refractive index of material in terms of wavelength is given by μ = a + b/λ2 + c/ λ4, Where a, b and c are constant for material.
Since wavelength of violet light is smaller than red light; from this formula it follows that the refractive index for violet light is more than for red light. μv > μr.
Thus different color of light emerge from the prism in different direction due to their wavelength.
Refractive index for yellow light is practically equals to mean of refractive index for violet and red light. μ = (μv + μr) / 2, for this reason yellow is called mean light.

Dispersive power of a prism

General meaning of dispersive power means the spread of the colors in the spectrum formed by the prism.
Dispersion is different from the deviation for a prism. Large dispersion means a large angle between original path of light ray (in absence of prism) and emerging ray after passing through prism.
Large deviation means a large angle between lights of different wavelengths after passing through the prism.
Dispersive power of the prism is the ratio of the dispersion to the deviation. In other words, it is the ratio of the difference in angle of deviation of any two colors to the angle of deviation of its mean color.
ω = δv - δR / δy = μv - μR / μy - 1
As the wavelength difference between colors of light is incident on a prism decreases, the ability of the prism to resolve them begin to weak.
Dispersive power of prism is more means the spread of colors in the spectrum formed by the prism will be large.
Dispersive power has no unit and it is strongly depends upon the material of the prism. For example dispersive power of flint glass prism is more as compared to crown glass prism.