Question

State and arrive at brewster’s Law in polarisation

Answer 1

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STATEMENT : -

Brewster's law of polarization states that, " The refractive index of a reflector is equal to tangent of the polarising angle. ."

Consider a polarizer with i(B) be the angle of polarization , 'n' be it's refractive index , then according to the law :

tan [i(B)] = n

So we have to prove that , tan [∅(p)] = n

PROOF :-

Consider a polarizer with an incident light ray on it with angle of incidence 'i' ,some light ray gets refracted with angle of refraction 'r'.

Let angle of incidence of polarizer be 'i(B) '.

Then by Snell's Law ,

n = sin i/sin r           and           n= sin i(B)/sin r _______(1)

=> sin i / sin r =  sin i(B) / sinr

=> i = i(B)

And we know that Brewster's angle of incidence ,

r + i(B) = 90

=> r = 90 - i(B)  ____________(2)

Substituting equation (2) in (1)

=> n = sin i(B) / sin [90-i(B) ]

=> n = sin i(B) / cos i(B)

=> n = tan i(B)

HENCE PROVED

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