How can light be partially polarized?

[orangeblue]

Homework Statement

I'm a new physics teacher and was teaching about polarization of light today. A student asked me a question I wasn't sure of the answer to.

Let's say you have two polarizing filters stacked on top of one another. The first filter is held so that the spaces in the filter are horizontal. The other is turned so the spaces in the filer are at a 45 degree angle.

What happens after light passes through the stacked filters?

Homework Equations

The Attempt at a Solution

I understand that when light leaves a source, its electric fields vibrate in all different planes. (Each individual light wave's electric fields vibrate in ONE plane, but this plane could be in any direction - correct?)

So after the light passes through the horizontal filter, it is horizontally polarized. This means its electric fields vibrate only in the horizontal plane.

Now, how can ANY of those horizontally polarized waves pass through the angled filter? The direction of the field vibration doesn't match the filter spacing, so wouldn't the light just get absorbed, the same as it would when you have a vertical and horizontal filter overlapped?

Also, I don't understand what happens to the magnetic field in this process. Are the magnetic fields unaffected by the polarizing filters?

 

[RedDelicious]

Why wouldn't some it pass through the angled polarizer? Unless the the polarizing axis of the second polarizer (called an analyzer) is set up orthogonally to the first, it's just a matter of geometry that some component of the polarized light will pass through through the second polarizer.

That is to say, if it's not completely orthogonal, then the polarized light must have a nonzero component parallel to the transmission axis of the polarizer. Components of the optical field parallel to transmission axis are going to be passed through without problem, hence why you can polarize light to begin with. You'll have the usual cosine dependence that arises in doing projections. The subsequent Intensity is described by Malus's Law.

What do you mean by the light waves electric fields? The polarization is described by the resultant E field. The plane of vibration can change in general.

What do you think happens to the magnetic fields? Where did the magnetic field come from in the first place?

 

[orangeblue]

I see - so because the electric fields can be broken down into orthogonal components, some component of the horizontally polarized light will make it through the angled filter. The component that is parallel to the filter lines makes it through. This explains why the light is dimmer after passing through the filter, right?

As for the magnetic fields, they arise from the changing electric fields. So now I see that if the electric fields don't make it through the polarizing filter, the magnetic fields won't either. (Couldn't it work the other way too though? Changing magnetic fields induce changing electric fields and vice versa. So could we approach this problem by looking at what polarizing filters do to the initial magnetic field and go from there?)

By light waves' electric fields I mean the changing electric field strengths that make up the light wave. I am still not sure if I am visualizing it right... as a single light wave moves from one place to another, does its electric field vibrate in the same plane the whole time? Or is the plane of vibration changing?

 

[RedDelicious]

I see - so because the electric fields can be broken down into orthogonal components, some component of the horizontally polarized light will make it through the angled filter. The component that is parallel to the filter lines makes it through. This explains why the light is dimmer after passing through the filter, right?

As for the magnetic fields, they arise from the changing electric fields. So now I see that if the electric fields don't make it through the polarizing filter, the magnetic fields won't either. (Couldn't it work the other way too though? Changing magnetic fields induce changing electric fields and vice versa. So could we approach this problem by looking at what polarizing filters do to the initial magnetic field and go from there?)

By light waves' electric fields I mean the changing electric field strengths that make up the light wave. I am still not sure if I am visualizing it right... as a single light wave moves from one place to another, does its electric field vibrate in the same plane the whole time? Or is the plane of vibration changing?

Yes.

Yes. The relationship between the electric and magnetic field doesn't change. It just natural to define it in terms of the electric field because it dominates the interactions.

No not in general. If it's confined to a single plane, you have plane polarized light. That is a special case. In general it can change, as it does in the case of circularly polarized light.

 

[orangeblue]

Thanks for your help!

I am still confused about the last paragraph you wrote. Once light becomes plane polarized, can it become unpolarized? What I mean is, right after passing through the filter, the light's electric fields vibrate in one plane only. Do they CONTINUE to vibrate only in that one plane always as the wave propagates? Or can the plane they vibrate in change some time after leaving the filter?

 

[RedDelicious]

Thanks for your help!

I am still confused about the last paragraph you wrote. Once light becomes plane polarized, can it become unpolarized? What I mean is, right after passing through the filter, the light's electric fields vibrate in one plane only. Do they CONTINUE to vibrate only in that one plane always as the wave propagates? Or can the plane they vibrate in change some time after leaving the filter?

No it doesn't become unpolarized. Un-polarizing would entail getting back part of the wave was already absorbed. I think the question you were intending to ask was if its polarization direction changes. No. For plane polarized light, the orientation of the E field is constant.

You keep saying light in general and so I just want to reiterate that the constant orientation is only true for plane polarized light. For different polarization states, it is not confined to a single plane and the plane changes as it propagates. I gave circularly polarized light as an example.

 

[orangeblue]

Thank you! You were right about the question I was intending to ask haha. It makes sense now after looking up some diagrams of circularly polarized light (which I had never heard of, so thanks for the example!)