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 angle of refraction in first face, r2 is the angle of incidence in 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 factor such as the angle of incidence, material of prism and angle of prism. And it is concluded that the angle of deviation decreases on gradually increasing the angle of incidence from 0, reaches a minimum angle and again increases. In the minimum position of Angle of deviation(δmin);
i = e, r1 = r2 = r
Then equation (iv) becomes,
r+r = A
r = A/2
Again equation (v) becomes,
δmin = i + i – A
δmin + A = 2i
i = (δmin + A)/2
From Snell’s law,
aµg = sin i / sin r
aµg= sin((δmin + A)/ 2)/ sin(A/2) ….. (ii)
Deviation through 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 angle of refraction in the first face, r2 is the angle of incidence in 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 in 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.
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