Refraction Through a Prism and Dispersion by a Prism

Refraction through a Prism

A light ray striking at one face of a triangular glass prism gets refracted twice and emerges out from the other face. The angle between the emergent and the incident rays is called the angle of deviation (D). The angle between the two refracting faces involved is called the refracting angle (A) of the prism.

r₁ + r₂ = A

D = (i - r₁) + (e - r₂)

Hence, A + D = i + e

Note: Keeping A+D constant, i and e can have two pairs of values such that value of i and e are interchanged in the two pairs.

Also, 

Minimum Deviation:

When the path of a light ray through the prism is symmetrical, then the angle of deviation is minimum.

So, angle of incidence = angle of emergence

i = e and r₁ = r₂

hence A + D_min= 2i

And A = 2r

from , we have:

Maximum Deviation: The angle of deviation is maximum when the angle of incidence or the angle of emergence is 90⁰.

Dispersion through a Prism:

The refractive index of a medium is different for light rays of different wavelengths. Larger the wavelength, the lesser is the refractive index. As a result light of different wavelengths deviates differently, splitting white light into its constituent colors. This is called dispersion.

i.e .,  because 

For a small refracting angle A, the deviation D is

Given by:

D ≈ (μ - 1) A

The angle between the red and violet rays called angle of dispersion is given by:

𝛟 = Dv - Dr = (μ_v - μ_r) A

The angle of mean deviation = 

Dispersive power of glass 

Combination of Prisms:

• When two prisms with an equal angle of dispersions are placed opposite to each other their dispersive effect is canceled.
  

• If we want to have only dispersion and no deviation, we combine two prisms having the same mean deviation.
  

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