Question

In the figure above, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of theta_1 = theta_2 = theta_3 = 41.5 degree with the direction of y axis. What percentage of the initial intensity is transmitted by the system of three sheets ? 48.526% 0.37131% 24.268% 0.732% 0.01103%

Answer 1

e) 0.01103%

Let Io is the intensity of unpolarized light.

Intensity through first polarizer, I1 = Io/2

Intensity through 2nd polarizer, I2 = I1*cos^2(theta)

= (Io/2)*cos^2(theta)

Intensity through 3rd polarizer, I3 = I2*cos^2(theta)

= (Io/2)*cos^2(theta)*cos^2(theta)

I3/Io = (cos^2(theta))^2/2

here the transmisiion angle between first and second polarizer,

the transmisiion angle between second and third polarizer = 2*41.5

= 83 degrees

= (cos^2(83))^2/2

= 0.0001103

= 0.01103 %