Question

Two polaroids are oriented at the angle phi to each other and a plane-polarized light is incident upon them. If the fraction eta of the incident light gets through both of them, what was the angle theta between the polarization direction of the light and the polarization axis of the first polaroid? After obtaining the formula for theta, calculate its numerical value for phi = 35 degree and eta = 0.1.

Answer 1

Let a plan polarized light of intensity I₀ is incident on first polarizer.

Then from law of malus-

                I=I₀ cos²(theta)

At second polarizer applying law of malus-

                I’=Icos²(phi)= I₀ cos²(theta) cos²(phi)

Also n=I’/I₀

                n= cos²(theta) cos²(phi)

                cos²(theta) = n/ cos²(phi)    

                theta=cos^-1(n^1/2/cos(phi) )

if phi=35⁰ and n=0.1

then

                cos(35⁰)=0.819

                theta=cos^-1(n^1/2/cos(phi) )

                theta= 67.29