Refraction through Prisms

 The phenomenon of  bending of light when it passes from one medium to another is called refraction of light. A prism is a transparent refracting medium bounded by two plane surfaces meeting each other along a straight edge.                                                       

Refraction through a Prism

In the given figure, surface AB and AC are the refracting surfaces.<BAC is the angle of prism and <LMQ is the angle of deviation.  Ray OP is the incident ray

 and QR is the emergent ray. Let A, B, C be the glass of the prism. Suppose BC is the base and AB and AC are its two refracting surfaces. From the above figure, we can say that OP is the incident. The ray traveling through the rarer medium and than the refractive index of the prism is the incident ray. As the ray PQ strikes the surface of the and it is called as the refracted ray. OR is the emergent ray which comes and When the ray light enters the glass, it bends towards normal and when ray comes out, it bends away from the normal. Now the angle between the emergent ray and incident ray is the angle of deviation. I₂=e.  For a single refracting surface,  δ = |i – r|

In this case, δ = (i1 + i2) – (r1 + r2)

δ = i1 + i2 – A, A is the angle between the prism between two lateral surfaces. We know that ∠A and ∠Q is 180º and Angle of the prism of (A) is r1 + r2

r1  is the angle of refraction inside the prism and r2 is the angle of refraction outside it.  Now substituting the values we get:

δ= i+e-A  

or, δ+A=i+e

Thus, when a ray is refracted through a prism, the sum of the angle of incidence and angle of emergence is equal to the sum of the angle of deviation and angle of prisms.

Minimum Deviation Condition

At a particular angle of incidence, the angle of deviation is minimum and this angle is called the angle of minimum deviation, δ_m.

As we know when a ray is refracted through a prism, the sum of the angle of incidence and angle of emergence is equal to the sum of the angle of deviation and angle of prism.

Angle of minimum deviation = δ_m

In this position, the angle of incident is equal to the angle of emergence, and angle of refection through first the refracted ray passes parallel to the base of an equilateral prism. So in minimum deviation position,

δ = δ_m, I = e

And r1 = r2 = r

We know,

A = r1 + r2

A = r1 + r2 = r + r

=2r

Or, r=A2………………………1

We know,

δ + A = I + e

Then;

δ_m = I + I + A

Or, 2i = A + δ_m

Or, i=A+δm2……2

From Snell’s law,

aµg = sinisinr

µ = {sin(A+δ_m)/2}/sin(A/2)_m
δ

thusffft

Thus, this is the relation between refractive index, angle of prism and angle of minimum deviation.

Deviation in Small Angle Prism

When a ray of light PQ making angle of incidence I incident on face AB, it is refraction in first face, r₂ is angle of incidence on RS. Here e is angle of emergence, r₁ is angle of refraction in first face, r₂ is angle of incidence on second face and δ is the angle of deviation. The angle of deviation of the ray of PQ is given by

δ = (I - r₁) + (e - r₂)

= (I + e) – (r₁ + r₂)……….1

At face AB,

µ = sinisinr1 

Since angle of incident is small then,

Equation  becomes

µ = ir1ir₁

Or, I = μ r₁

Similarly at face AC,

e=μ r₂

Substituting value of I and e in 1 we get

                          =(μ−1)(r1+r2)=(μ−1)(r1+r2)

= (μ -1) A, where r₁ + r₂ + A

δ = (μ -1) A

That is angle of deviation of a ray is independent with angle of incidence in a small angled prism.

Grazing Incidence and Grazing Emergence

When a ray of light is incident on a face of a prism with an angle of incidence 90^o , the ray lies on the surface and is refracted through the prism. This refraction of the prism is called the grazing incidence.

 A condition in which an emergent ray is perpendicular to the normal of the emergent surface of a medium or a condition in which an emergent ray makes an angle of almost 90° from the normal to the emergent surface of a propagation medium is called grazing emergence.