ETSM Presentation

8/6/2019 ETSM Presentation

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STRESS OPTIC

LAW

Aishwarya Ramesh

R180208005

B.Tech ASE (3rd Year)


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Birefringence

When polarized light passes through a stressedmaterial the light separates with two wavefronts

travelling at different velocities, each oriented

parallel to the direction of principal stresses (1

,2) in the material, but perpendicular to eachother.

Light traveling through a birefringent medium will take one of twopaths depending on its polarization.


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Birefringence

Birefringence results in the stressed material

having two different indices of refraction (n1 ,

n2).

In most material, the index of refraction

remains constant, however in glass and

plastics the index value varies as a function

of the stress applied. This gave rise to theStress Optic Law.


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Stress Optic Law

(n1-n2) = CB (1-2)

Where

n1, n2 = Indices of refraction

CB = Stress optical constant

1, 2 = Principal stresses


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Stress Optic Law

This law establishes that birefringence

directly proportional to the difference of

principal stresses which is equal to

difference between two indices of refraction(n1-n2) exhibited by a stressed material .

Therefore birefringence can be calculated by

determining

n.


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Derivation of Stress Optic Law

ExpressionLet n1, n2 be the principals of refractive

indices for waves vibrating parallel to the

principal stresses 1, 2 respectively at anypoint in a stressed material and let n0 be the

index of refraction for the unstressed

material. Then according to Maxwell, the

relationship between the principal refractiveindices and the principal stresses are:


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n1 n0 = C1 1+C2 2

n2 n0 = C1 2 + C2 1

Where C1 and C2 are constants depending

on the material and may be called stress

optic coefficients.Subtracting, we get

n1-n2 = (C1-C2) (1-2)

Let C1 C2 = CB = relative or differentialstress optic coefficient,

Therefore,

(n1-n2) = CB (1-2)


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Now the wave equation is

y = a sin (z + t) = a sin

Angular phase shift

= 1 2

Assuming the stressed model to behave like

a temporary wave plate, we have

1 = (n1 n0)

2 = (n2 n0)


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So,

= 1 2 = (n1 n2)Where,

h = thickness of the model

Thus,n1 n2 =

Hence we get

= CB (1-2)

= CB (1-2)

(1-2)


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Thus we can summarize photoelastic effect

laws as:

The light on passing through a stressed

model becomes polarized in the direction

of the principal stress axes and is

transmitted only on the planes of theprincipal stresses.

The velocity of the transmission in each

principal plane is dependent on theintensity of the principal stresses in these

planes.


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