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Problem #4: Stack of Polarizers fun and LCD! We know that the relationship between the input...

Problem #4: Stack of Polarizers fun and LCD! We know that the relationship between the input and output intensity of a polarized light or E&M wave for an ideal polarizer is given by Malus Law: 1I, cos (0), where θ is the angle between the polarizer axis and the polarization direction of the incident wave. A) Suppose we have two polarizers at 45 degrees to each other. What is the output intensity as a function of the input polarization angle? Suppose we have two polarizers at 90 degrees to each other. What is the output intensity now? Suppose, we added a third polarizer to B, rotated at 45 degrees to the first polarizer. What is the output intensity now? Now, take N+1 polarizers, and arrange them so that the n=1 and n=N+1 polarizers are at 90 B) C) D) degrees to each other. The n-2 polarizer is rotated relative to the n=1 polarizer by #22N and n=3 is rotated the same angle relative to the n-2, etc., and so on and so forth such that the total rotation angle is θ= N39 = Find the output intensity in the limit of large N or N →。。

Problem #4: Stack of Polarizers fun and LCD! We know that the relationship between the input and output intensity of a polarized light or E&M wave for an ideal polarizer is given by Malus' Law: 1I, cos (0), where θ is the angle between the polarizer axis and the polarization direction of the incident wave. A) Suppose we have two polarizers at 45 degrees to each other. What is the output intensity as a function of the input polarization angle? Suppose we have two polarizers at 90 degrees to each other. What is the output intensity now? Suppose, we added a third polarizer to B, rotated at 45 degrees to the first polarizer. What is the output intensity now? Now, take N+1 polarizers, and arrange them so that the n=1 and n=N+1 polarizers are at 90 B) C) D) degrees to each other. The n-2 polarizer is rotated relative to the n=1 polarizer by #22N and n=3 is rotated the same angle relative to the n-2, etc., and so on and so forth such that the total rotation angle is θ= N39 = Find the output intensity in the limit of large N or N →。。
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Answer #1

from the Malus law

(a)

I_out = I_0 cos^2 theta

I_out =I_0 cos^2 45

(b)

I_out = I_0 cos^2 90 = 0

(c)

I_3 =I_0 cos^2 45

     =0.5 I_0

I_out put = I_3 cos^2 45 = 0.5 I_0 ( 0.5) = 0.125 I_0

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