Polarizing Filters Fraction of Light Passing Through

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In summary, the unpolarized light passes through all four filters with a fraction of intensity equal to (.2053).
  • #1
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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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  • #2
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.
 
  • #3
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.
 
  • #4
Try thinking about what is actually happening at the first filter - remembering that the light arriving at the first filter is unpolarised.
 
  • #5
The orientation of the light is changed by 25 degrees, correct?
 
  • #6
What is the orientation of unpolarised light?
 
  • #7
Isn't it all random?
 
  • #8
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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  • #9
Oh okay I got it, so I was using the wrong equation for the first step. Thanks!
 

What is a polarizing filter?

A polarizing filter is a type of camera filter that is used to reduce glare and reflections from non-metallic surfaces such as water, glass, and foliage. It works by only allowing light waves that are aligned in a specific direction to pass through, resulting in a clearer and more contrasted image.

How do polarizing filters work?

Polarizing filters work by using a special material that is made up of long, thin molecules that are aligned in a particular direction. When light waves enter the filter, they are only allowed to pass through if they are aligned in the same direction as the molecules. This causes the filter to block out certain light waves, resulting in reduced glare and reflections.

What are the benefits of using a polarizing filter?

The main benefit of using a polarizing filter is to reduce glare and reflections in your photographs. This can result in clearer and more vibrant images, especially when photographing water, landscapes, and other reflective surfaces. Polarizing filters can also help to enhance the contrast and color saturation in your photos.

When should I use a polarizing filter?

Polarizing filters are most commonly used in outdoor photography, particularly when photographing landscapes, water, and other reflective surfaces. They can also be useful in reducing glare and reflections in architecture and product photography. However, it's important to note that polarizing filters work best when the light source is coming from a specific direction, so they may not be as effective in low light or indoor settings.

Do polarizing filters work on all types of cameras?

Yes, polarizing filters can be used on all types of cameras, including DSLRs, mirrorless cameras, and even smartphones. However, the filter you choose must be the correct size for your lens, so it's important to check the diameter of your lens before purchasing a polarizing filter. Additionally, some compact cameras and smartphone cameras may not have a thread on the lens to attach a filter, so be sure to check your camera's specifications before buying a filter.

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