Polarizing Filters Fraction of Light Passing Through

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Unpolarized light passing through four polarizing filters with a 25-degree offset between each results in a specific fraction of light transmission. The correct approach involves calculating the intensity after each filter using the formula I=I0Cos²θ, starting with the initial intensity of unpolarized light. The intensity after the first filter is halved, as unpolarized light becomes polarized, and subsequent filters require adjusting the angle based on the previous filter's orientation. The user initially misapplied the equations, leading to an incorrect final fraction of light. Understanding the transition from unpolarized to polarized light and correctly applying the angle adjustments is crucial for solving the problem accurately.
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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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