Calculating Intensity of Unpolarized Light with Polarizers

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In summary, when light passes through a polarizer, the intensity decreases by a factor of 1/2 if the transmission axis is rotated 18 degrees from the vertical.
  • #1
hardwork
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PART 1: Unpolarized light has an intensity of 100 W/m^2. It passes though a polarizer whose transmission axis is rotated 18 degrees with respect to the vertical. What is the intensity of the light that emerges from the polarizer?

I = (1/2)(Io)(cos angle)^2
I = (1/2)(100 W/m^2)(cos 18)^2
I = 45 W/m^2 -- I am not sure if this is correct.

PART 2: This light passes through a second polarizer and the intensity of the light that emerges is 40 W/m^2. What angel does the transmission axis of the second polarizer make with the vertical?

I don't understand this part. Would I use the same equation above and plug in 40 W/m^2 for I, 100 W/m^2 for Io, and solve for cos?

Thank you!
 
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  • #2
PART 1: From a polarizer 50% of light will be transmitted irrespective of the orientation of the transmission axis.
For part 2, use Malus's law.
 
  • #3
Thank you!
For PART 1, would it just be I = (1/2)(100 W/m^2) then? So, I = 50 W/m^2 ?
I still don't understand PART 2. What do I plug into Malus' Law?
 
  • #4
I = Imax*cos^2(theta)
 
  • #5
Part 1 is okay then? The answer is 50?

Part 2: 40 W/m^2 = 100 W/m^2 cos^2(theta)
and then solve for cos?
 
  • #6
hardwork said:
Part 1 is okay then? The answer is 50?

Part 2: 40 W/m^2 = 100 W/m^2 cos^2(theta)
and then solve for cos?
No.
For second polarizer Imax is 50 w/m^2
 
  • #7
Oh! Thank you so much for helping me. I'm sorry I'm a little confused.
Would the answer be 27 degrees?

I am not sure if I solved for the angle correctly. I'm forgetting my math skills here. haha
 
  • #8
Part 2: 40 W/m^2 = 50 W/m^2 cos^2(theta)
cos^2(theta) = 0.8
Find cos theta. Add 18 degrees to this angle to get the result.
 
  • #9
cos^2(theta) = 0.8
then take the sqrt of both sides?
cos(theta) = 0.9
cos-1(theta) = 26 degrees

Angle: 26 + 18 = 44 degrees ... I hope. :redface:
 
  • #10
Yes. Correct. You can take 26.6 as well.
 
  • #11
That was very helpful. Thanks, again!
 

1. How do I calculate the intensity of unpolarized light with polarizers?

To calculate the intensity of unpolarized light with polarizers, you will need to know the initial intensity of the light source, the angle of the polarizer relative to the direction of polarization, and the angle of the analyzer relative to the direction of polarization. You can then use Malus' law to calculate the final intensity of the light after passing through the polarizer and analyzer.

2. What is Malus' law?

Malus' law states that the intensity of polarized light passing through a polarizer is equal to the initial intensity of the light multiplied by the cosine squared of the angle between the polarizer and the direction of polarization. This law can be used to calculate the intensity of unpolarized light after passing through a polarizer and analyzer.

3. Can I use Malus' law for any type of polarized light?

Malus' law can be used for any type of polarized light, as long as the polarizer and analyzer are aligned with the same direction of polarization. However, it may not accurately predict the intensity of partially polarized light, as it assumes a perfect polarization state.

4. How does the angle of the polarizer and analyzer affect the intensity of unpolarized light?

The angle of the polarizer and analyzer relative to the direction of polarization can greatly affect the intensity of unpolarized light. When the angles are perpendicular to each other, the intensity will be at its minimum. As the angles approach being parallel, the intensity will increase and reach its maximum when the angles are aligned with each other.

5. Is it possible to calculate the intensity of unpolarized light without using polarizers?

No, it is not possible to calculate the intensity of unpolarized light without using polarizers. Unpolarized light is composed of waves with different directions of polarization, and polarizers are necessary to filter out specific directions of polarization in order to measure the intensity of the remaining light.

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