REFRACTION THROUGH PRISMS

Prism

    A Prism is a transparent refracting medium bounded by two plane surfaces meeting each other along a straight edge.

 Refraction through prism

Let JKL be a prism with refractive angle A. A ray of light PQ is incident on face JK at an angle i. This ray is refracted along QR in the prism and finally emerges out along RS. Here, r₁ is the angle of refraction in the first face, r₂  is the angle of incidence in the second face, and e is the angle of emergence through the second face. The angle δ between the direction of incidence and the emergent ray is called the angle of deviation. 

MN and ON are the normal drawn on refracting surfaces JK and JL respectively.

The angle of deviation on the first face JK is

δ₁ = <TQR

    = <TQN - <RQN

    = i – r₁

The angle of deviation on the second face JL is

δ₂ = <TRQ

    = e – r₂

Since the deviation are in the same direction at two faces, the net deviation produced by the prism is

δ = <RTL

  = δ₁ + δ₂

  = i+e – (r₁+r₂) ………. (i)

In ΔQNR,

<NQR + <QRN + <QNR = 180

r₁ + r₂ + <QNR = 180

r₁ + r₂= 180 - <QNR ……… (ii)

In quadrilateral QJRN

QJN + JRN + NQJ + RNQ = 360

<A + 90 + 90 + <QNR = 360

<A = 180 - <QNR ……. (iii)

From equation (ii) and (iii),

<A = r₁ + R₂ …… (iv)

Putting in equation (i),

δ = i + e - A ……. (v)

R.I. of Prism using minimum deviation

Experimentally, it is found that the angle of deviation depends on factors such as the angle of incidence, the material of the prism, and the angle of prism. And it is concluded that the angle of deviation decreases gradually increasing the angle of incidence from 0, reaching a minimum angle, and again increasing. In the minimum position of Angle of deviation(δ_min);

i = e, r₁ = r₂ = r

Then equation (iv) becomes,

r+r = A

r = A/2

 Again equation (v) becomes,

δ_min = i + i – A

δ_min + A = 2i

i = (δ_min + A)/2

From Snell’s law,

aµg = sin i / sin r

aµg= sin((δ_min + A)/ 2)/ sin(A/2) ….. (ii)

Deviation through the small angled prism
         Consider a prism ABC of small-angle A. A ray of light PQ is incident on face AB at an angle i. This ray is refracted along QR in the prism and finally emerges out along RS. Here, r₁ is the angle of refraction in the first face, r₂ is the angle of incidence in the second face, and e is the angle of emergence through the second face.

 We know, δ = (i-r₁) + (e + r₂) = (i+e) – (r₁ + r₂) ………. (i)

At face AB,

µ = sin i / sin r₁ …… (ii)

Since angle of incident is very small, sin i is nearly equal too i, and sin r is nearly equal to r

µ = i / r₁

i = µr₁

At face AC,

µ = e/ r₂

e = µr₂

substituting value of i and e in equation (i), we get

δ = µr₁ + µr₂ - (r₁+r₂)

δ = µ (r₁ + r₂) – (r₁ + r₂)

δ = (r₁ + r₂) (µ - 1)

δ = A (µ - 1) [.: r₁+r₂ = A]

Grazing Incidence and Grazing Emergence

Grazing Incidence: When a ray of light is incident on the face of a prism with an angle of incidence 90, the ray lies on the surface of the prism and gets refracted through a prism. The refraction of a prism is called grazing incidence.

Grazing Emergence:  When an emerging ray of light emerges out making an angle of 90 and grazes out through the surface of the prism, it is Grazing Emergence.