Question

Derive : Refraction and Dispersion of Light Through a Prism.

Answer 1

Angle of Deviation:

Angle of deviation (δ) is the angle between 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

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 traveling 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.

Hope THIS HELPS you

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