Unpolarized light with an intensity of 865 W/m^2 is incident on a polarizer with

Question

Unpolarized light with an intensity of 865 W/m^2 is incident on a polarizer with an unknown axis. The light then passes through a second polarizer with has an axis which makes an angle of 71.0 degree with the vertical. After the light passes through the second polarizer, its intensity has dropped to 181 W/m^2. What is the angle between the axes of the polarizers? Unpolarized light of intensity I_0 is incident on three polarizing filters. The axis of the first is vertical, that of the second is 30 degree from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?

Explanation / Answer

Q1.

when the unpolarized light passes through the first polarizer, as per Malus law,

intensity becomes 0.5 times original intensity.

so intensity=865/2=432.5 W/m^2

when light passes through second polarizer, its intensity becomes cos^2(theta) times intensity

where theta=angle between the axis of two polarizers

==>181=432.5*cos^2(theta)

==>theta=49.691 degrees

so angle between the axis of polarizers is 49.691 degrees.

Q2.

intensity after first polarizer=0.5*I0 (as the initial light is unpolarized)

intensity after second polarizer=intensity after first polarizer*cos^2(theta)

where theta is angle between axes of two polarizers

==>intensity after second polarizer=0.5*I0*cos^2(30)

=0.375*I0

intensity after third polarizer=0.375*I0*cos^2(90-30)

=0.09375*I0

so answer is 0.09375

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