Unpolarized light passes through three polarizing filters. The first filter has

Question

Unpolarized light passes through three polarizing filters. The first filter has its transmission axis parallel to the z direction, the second has its transmission axis at an angle of 30 degrees from the z direction, and the third has its transmission axis at an angle of 60 degrees from the z direction. If the light that emerges from the third filter has an intensity of 693 W/m^2, what is the original intensity of the light? ( assume both angles are measured in the same direction from the +z axis)

Explanation / Answer

let,

original intensity Io=1810 W/m^2

theta1=0 degerees,

theta2=30 degrees,

theta3=60 degrees

use,

I=Io*cos^(theta)

after first polarizer,

I1=Io*cos^(0)

I1=Io

I1=Io

now,

after second polarizer,

I2=I1*cos^(theta2-theta1)

I2=Io*cos^2(30-0)

I2=0.75*Io W/m^2

and

after 3rd polarizer,

I3=I2*cos^(theta3-theta2-thet1)

693=0.75*Io*cos^2(60-30-0)

=====> Io=1232 W/m^2

initial intensity, Io=1232 W/m^2

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