# Polarized light filtering question.

1. Oct 24, 2008

### HooDude

Hello all, i'm new to the board here.

I have been scratching my head over an example in one of the books I was reading so I looked it up on google. I found an explanation differing from what i'd read, so I thought I would pose the question to this community and see what you think.

I have no real physics experience beyond highschool, but i've been reading books for interest sake. The book I was reading that prompted this question is "The God Effect" by Brian Clegg, First Edition. On page 60 there is a description and diagram of what happens when light passes through a series of polarized filters. If unpolarized light passes through a horizontal filter and then meets a vertical filter, no light passes through the vertical filter. However, if a 45 degree polarized filter is placed between the horizontal and vertical filters, there is some light that makes it through all three filters.

The book states that light that passes through the first (horizontal) filter becomes horizontally polarized. Thus this light cannot pass through the vertical filter. However, the act of placing the 45 degree filter in line causes photons of the light to be changed so as to have a 50:50 chance of being vertically or horizontally polarized. Thus, 50% of the light to pass through the 45 degree filter will make it through the final vertical filter.

I then found a website claiming that the filters actually change the direction of the wavelengths of light, reducing their magnitude more and more the further away from the degree of polarization the initial light is. Thus light gets squished into 0 degrees, then cannot pass through a 90 degree filter. But when you place the 45 degree filter in, the 0 degree light gets squished to 45 degrees, then that light gets squished further to 90 degrees.

It seemed to me that the first explanation had to do with the probability of a photon being polarized in any direction. That the first filter removes all the non-horizontally polarized photons, and that then the 45 degree filter somehow effects the photons so that they now have a probability of being either vertically or horizontally polarized; allowing the vertical ones to pass though the final filter. But I can't see how this works, honestly.. it doesn't sit well with me. The website explanation seems better. Am I just missing something fundamental? Are these two explanations really saying the same thing?

What is the correct explanation? Sorry for being a physics nub :P at least i'm interested!

Last edited: Oct 24, 2008
2. Oct 25, 2008

### pallidin

I'm no expert, but remember that those are "filters", allowing only such light to pass through which has the same polarization orientation as the filter itself.

There are materials that can actually change polarization when an electric field is applied, but I don't think that's what your asking.

3. Oct 25, 2008

### Staff: Mentor

You can explain the action of a polarizing "filter" using a quantum mechanical view (which is what first explanation attempted) or a classical view (as done on that website). Both explanations are "equivalent"--they lead to the same conclusions--but it sounds like the first explanation did not do a good job explaining things.

From a quantum viewpoint, think of each of the "unpolarized" photons as having a being in a 50/50 superposition of "vertical" and "horizontal" states. (That's a bit of a simplification. The photons will be in all sorts of states, but on average they will have a 50/50 mix of "vertical" and "horizontal".) When such a photon encounters a horizontal polarizer, it has a 50% probability of being passed (or blocked). Once it passes through the polarizer, its "state" becomes purely "horizontal".

But that "horizontal" state can be viewed as a 50/50 superposition of "45 degree" and "135 degree" states. So when the "horizontal" photon encounters a 45 degree filter, it has a 50% probability of being passed (or blocked). A photon that passes through that filter becomes purely "45 degrees".

But that "45 degree" state can be viewed as a 50/50 superposition of "vertical" and "horizontal" states. So when the photon now encounters a vertical polarizer, it has a 50% probability of being passed (or blocked). If it hadn't passed through that 45 degree polarizer it would have been purely "horizontal" and would have 0 chance of passing through a vertical filter.

I hope that makes a little sense.

As the website points out, the use of the term "filter" is problematic, as it implies a passive sieve-like action. But (taking the classical view) the filter changes the angle of the electric field of the light passing through it; (taking the quantum view) it changes the state of the photon that passes through it.

Last edited: Oct 25, 2008
4. Oct 25, 2008

### HooDude

Thank you both for your replies. That explanation makes perfect sense Doc Al. The author didn't explain the concept at all. Thanks again for the help!

5. Oct 25, 2008

### Danger

Doc Al, that was a great post. I never thought that I would understand anything about optics, since it's so mathematical in nature, but your explanation was clear, concise, and math-free. Thanks.