Polarizing Filters Fraction of Light Passing Through

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Homework Help Overview

The problem involves unpolarized light passing through four polarizing filters, each oriented at an angle of 25 degrees relative to the previous one. The objective is to determine the fraction of light that successfully transmits through all filters.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the intensity of light after each filter and the correct application of the equations involved. There is an exploration of how the angle between filters affects the light's polarization and intensity.

Discussion Status

Participants are actively engaging with the problem, questioning their assumptions about the angles and the nature of unpolarized light. Some guidance has been offered regarding the step-by-step approach to analyzing the light's behavior through the filters, and there is recognition of the need to reconsider the initial conditions of the light.

Contextual Notes

There is a mention of a previous similar problem worked out in class, which may influence participants' expectations and approaches. The discussion reflects uncertainty about the correct equations and the interpretation of the angles involved.

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Homework Statement


Unpolarized light passes through 4 polarizing filters. The polarizing direction of each filter is offset by 25 degrees from the filter in front of it. Find the fraction of light that gets through all four filters.

Homework Equations


I=I0Cos2θ

The Attempt at a Solution


From my class notes, the professor worked a very similar problem in which there were two polarizing filters. He used (1/2)I0Cos2θ to solve for the answer. So I used (1/4)I0Cos2θ and got .2053, and the answer is supposed to be .277. Can someone please explain what I am doing wrong here?
 
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Think of this problem step by step rather than just finding an equation to plug things into: How much intensity remains after the first filter? How much after the second? How (in what polarisation) does the light arrive at the second filter? How does it arrive at the third? What is then the intensity after the third? Etc.
 
Okay so I tried solving that equation each time for every filter. I started with simply cos(25)^2, Then used the answer as I0 for the next filter (So .82139*Cos(25)^2) etc.. I am still getting the wrong answer. Does the angle itself change between each filter? My interpretation is that the angle is 25 degrees between each filter.
 
Try thinking about what is actually happening at the first filter - remembering that the light arriving at the first filter is unpolarised.
 
The orientation of the light is changed by 25 degrees, correct?
 
What is the orientation of unpolarised light?
 
Isn't it all random?
 
Exactly, but the light exiting the first filter is not. So if you have unpolarised light before the first filter, what is the intensity after? (We have already settled that it will be polarised after, then you can think of what happens to the polarised light when it passes the remaining filters.)
 
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Oh okay I got it, so I was using the wrong equation for the first step. Thanks!
 

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