Question

For the polarizers in the figure below, suppose the incident light is linearly polarized, the transmitted intensity (through both polarizers) is 0.19 ? I0, and the axis of second polarizer makes an angle ? = 54° with the axis of the first polarizer. What is the angle the initial direction of polarization makes with the first polarizer?

Answer 1

let Io is the intensity of linearly polarized light.

given

theta2 = 54 degrees

theta1 = ?

Intensity through first polarizer,

I1 = Io*cos^2(theta1)

Intensity through second polarizer,

I2 = I1*cos^2(theta2)

0.19*Io = Io*cos^2(theta1)*cos^2(theta2)

0.19 = cos^2(theta1)*cos^2(theta2)

cos^2(theta1) = 0.19/cos^2(theta2)

cos^2(theta1) = 0.19/cos^2(54)

cos^2(theta1) = 0.5499

cos(theta1) = sqrt(0.5499)

cos(theta1) = 0.7416

theta1 = cos^-1(0.7416)

= 42.1 degrees <<<<<<<<<---------------------Answer