Important Physics Notes on Dispersion of Light

What is Dispersion Of Light?

‘Dispersion of Light’ can be defined as the splitting of white light when it passes through a glass prism into its constituent spectrum of colours (i.e. violet, indigo, blue, green, yellow, orange and red). Dispersion figuratively means ‘distribution’ and hence that’s exactly what is happening in the picture above. The white light splits into its constituent colours at various frequencies and various angles.

Prism

A prism is a transparent refracting device bounded by five plane surfaces inclined at some angles. It bends the light two times and emergent ray is at an angle to the incident ray.

The angle of Deviation:

The angle of deviation (δ) is the angle between the emergent ray and incident ray.

For a single refracting surface, δ=|i−r|

For a prism, δ=(i1+i2)−(r1+r2)

δ=i1+i2−A

Where A is the angle of the prism. For angle of minimum deviation, δ is minimum and i1=i2=i

δmin=2i−A

For small A , δ=(μ−1)A

Dispersion of White Light By a Prism

Refraction is the bending in the path of the light when it travels from one medium to the another. The degree at which refraction will occur depends on the wavelength of the light. Each light wave has a different wavelength and will therefore deviate differently. White light is composed of light of different wavelengths (colors) i.e. violet, indigo, blue, green, yellow and red. Red has the highest wavelength and violet the lowest.

Wavelength is inversely proportional to the deviation in the path of the light. Red light suffers the least amount of deviation and violet the most. When a white light is made to pass through a prism, formation of a spectrum of seven colors occurs showing white light is a combination of seven separate colors.

Prism only acts as a medium for the dispersion of light made of the seven colors. Refraction occurs when the light falls on the prism. The wavelength and frequency of these deviated colors is different, they deviate differently at different angles due to the velocity difference of the prism. The color red therefore deviates the least since it has maximum wavelength and color violet deviates the most since it has the least wavelength.

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Refraction of Light through a Glass Prism

A glass prism has 3 rectangular lateral surfaces and 2 triangular bases, all inclined at an angle. This angle is called the ‘Angle of the prism’. Let’s take a triangular prism with a ray of light entering it.

In the figure, D is the angle of the prism.

Snell’s law mentions that when travelling from a rarer medium to a denser medium-light bends towards the normal, and bends away from the normal when traveling from denser medium to rarer medium. Here glass is denser than air, and therefore, when the light ray falls on the surface of the prism, the ray of light bends towards the normal. Hence according to the figure, when ray JP falls on the surface of the prism ,it bends towards the normal GP.

The emergent ray ON while moving from glass to air, it bends away from the normal. The angle of deviation, ∠XFN gives us the degree at which the emergent ray has deviated from the incident ray. The anagle of deviation is minimum when the angle of incidence is equal to angle of emergence. In the diagram given, ∠JPG = ∠YPN and ∠XFN is the angle of deviation, which is minimum. In this case the refracted ray PO is parallel to side EF.

This is how when passing through a prism, dispersion of light (white light) happens wherein it splits into it’s seven constituent colours. Different colors of different wavelength experience different degree of deviation and hence when put through refraction,white light splits into its constituent colors.

Dispersion of Light and Rainbow

A rainbow is formed when it rains and there’s sunshine simultaneously. Each raindrop is made of a different shape and has a different consistency as compared to a glass prism, still it affects light in a similar fashion. One can see the seven constituent colors (red, orange, yellow, green, blue, indigo and violet) when white light (sunlight) hits a collection of raindrops at a fairly low angle.

When the white sunlight travels from air into the drop of water, the constituent colors of light slow down to varying speed and frequencies. When violet light enters the raindrop it bends at a relatively sharp angle. Some of the light then passes back out into the air, and the rest is reflected back. Some of that reflected light passes out of the drop, bending as it moves back into the air again.

This way, each raindrop disperses the white sunlight into its constituent colours. We see a wide band of color as if different rainy areas were dispersing a different single color since we only see one color from each raindrop.

Sometimes we also see a double rainbow — a sharp rainbow with a fainter rainbow above it. The fainter rainbow occurs in the same manner as the sharper rainbow, but here the light is reflected twice inside the raindrop instead of reflecting once. Due to this double reflection, the light exits the raindrop at different angles, so we see it above the sharper rainbow. And if you observe carefully, you’ll notice that the colors in the secondary rainbow are in the reverse order of the primary rainbow.

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