Light travelling through several polarizers

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In summary, the problem involves three polarizers arranged in a straight line, with one spinning in the middle at an angle θ=ωt. The goal is to find the intensity of light coming out the other side as a function of time. Using Manus's Law, the attempt at a solution results in Imax/8 (1- cos(4ωt)), but the book expects Imax/16 (1- cos(4ωt)). The discrepancy could be due to a typo or miscalculation.
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Homework Statement


This is problem 71, chapter 38 in Physics for Scientists and Engineers 8th edition by Serway/Jewett.

Three polarizers are situated in a straight line with one spinning in the middle with θ=ωt.
Find the intensity of light coming out the other side as a function of time.
The attachment is the diagram of the system.

Homework Equations


Manus's Law: I = Imax cos2 θ. Where θ is the angle between the transmission axis for the two polarizers.

The Attempt at a Solution


Through the first two polarizers we have:
I= Imax cos2 θ = Imax cos2 ωt
which becomes
I= Imax/2 (1+ cos(2ωt))

Then the light from the second polarizer is:
I= Imax/2 (1+ cos(2ωt)) cos2 (90-ωt)= Imax/2 (1+ cos(2ωt)) sin2 (ωt)

and this turns into:
Imax/4 (1+ cos(2ωt))(1- cos(2ωt))
Imax/4 (1- cos2 (2ωt))
Imax/4 (1-(1+cos(4ωt)/2))
And for the answer we have:
Imax/8 (1- cos(4ωt))

The problem is the book expects the solution to be:
Imax/16 (1- cos(4ωt))

So I am off by a factor of 2. Can anyone see my problem or could it be a typo?
 

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  • #3
Must not have clicked upload the first time.
 
  • #4
What would the intensity be with only one polariser?
 
  • #5
*face to palm* Thanks Haruspex
 

1. How does a polarizer affect the intensity of light passing through it?

A polarizer is a material that filters light based on its orientation. When light passes through a polarizer, it only allows light waves with a certain orientation to pass through, blocking all others. This results in a decrease in intensity of the light passing through the polarizer.

2. Can multiple polarizers be used together?

Yes, multiple polarizers can be used together to further filter the light. The second polarizer will only allow the light that has passed through the first polarizer to pass through, resulting in an even lower intensity of light.

3. How does the angle of the polarizer affect the intensity of light passing through it?

The angle of the polarizer affects the intensity of light passing through it because it determines the orientation of the light waves that are able to pass through. If the angle of the polarizer is perpendicular to the light waves, it will block all of the light and result in no intensity. As the angle of the polarizer changes, the intensity of light passing through it will also change.

4. Can polarizers affect the color of light passing through them?

Yes, polarizers can affect the color of light passing through them. This is because different colors of light have different orientations, and a polarizer will only allow light with a certain orientation to pass through. This results in a change in the color of light that is transmitted through the polarizer.

5. How does the number of polarizers affect the intensity of light passing through them?

The number of polarizers used in a series will greatly affect the intensity of light passing through them. Each polarizer will filter out a certain amount of light, resulting in a decrease in intensity with each additional polarizer. However, if the polarizers are oriented in the same direction, the intensity of light passing through them will remain constant.

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