Polarization of Light Analogy Question

[flintstones]

Homework Statement

Hi everyone,

I'm a high school teacher and every time I teach the concept of polarization, students ask me the same question and I can't answer it.

I show students this picture. The red lines show the electric field vibrations. After passing through polarizer 1, the electric field is vibrating vertically. Since the magnetic field is 90 degrees to the electric field, the magnetic field is vibrating horizontally.

Therefore, shouldn't the magnetic field make it through polarizer 2? It obviously doesn't but I'm not sure why not. Students always ask me this and I have no answer for them.

Homework Equations

The Attempt at a Solution

I have a feeling the answer is something to do with Maxwell's equations, but we don't teach those at the high school level. I'm not sure how to resolve this one. If I had to guess, I'd say the magnetic field is still there but its amplitude is zero? But I'm not really sure why.

 

[Delta2]

If the magnetic field would make it alone through the second polarizer, without the accompanying E-field, then this would violate Maxwell's equations. One of the implications of Maxwell's equations is that an E-field wave is always accompanied by a B-field wave and vice versa. The only case that we can have a stand alone E-field is then the E-field is static(electrostatic case), and the only case we can have a standalone B-field is when the B-field is static(magnetostatic case)

 

[doggydan42]

Homework Statement

Hi everyone,

I'm a high school teacher and every time I teach the concept of polarization, students ask me the same question and I can't answer it.

I show students this picture. The red lines show the electric field vibrations. After passing through polarizer 1, the electric field is vibrating vertically. Since the magnetic field is 90 degrees to the electric field, the magnetic field is vibrating horizontally.

Therefore, shouldn't the magnetic field make it through polarizer 2? It obviously doesn't but I'm not sure why not. Students always ask me this and I have no answer for them.

View attachment 234472

Homework Equations

The Attempt at a Solution

I have a feeling the answer is something to do with Maxwell's equations, but we don't teach those at the high school level. I'm not sure how to resolve this one. If I had to guess, I'd say the magnetic field is still there but its amplitude is zero? But I'm not really sure why.

A changing electric field induces a magnetic field, and a changing magnetic field induces an electric field. If the magnetic field passes through polarizer 2, then that changing magnetic field would induce an electric field and there would be light, but the light vanishes because both the electric and magnetic fields vanish.

Another possible way to explain it would be to try to identify what happens to the magnetic field as it passes through a polarizer. Try looking at the case where already vertically polarized light passes through a vertical polarizer. Then, take the case where vertically polarized light passes through a horizontal polarizer. The results of these cases would help determine what happens to the magnetic field.

Keep in mind that the electric field should be perpendicular to the magnetic field.

 

[haruspex]

Assuming a wire grid polarizer, if the plane of the electric field is parallel to the wires then the wires interfere with it. The field is unable to induce a voltage along them, so the wave is reflected in the same way as a sound wave at the end of a tube. The wires do not interact with the magnetic field.

 

[Delta2]

Assuming a wire grid polarizer, if the plane of the electric field is parallel to the wires then the wires interfere with it. The field is unable to induce a voltage along them, so the wave is reflected in the same way as a sound wave at the end of a tube. The wires do not interact with the magnetic field.

Just to add to the bold section something that I consider important. The wires do not interact with the magnetic field in a direct way. Indirectly they interact via the coupled E-Field, (so that if the E-field wave is reflected then its coupled perpendicular B-Field wave is also reflected).

 

[flintstones]

Thank you for the replies, everyone! After reading your replies I think I had a misunderstanding of what a polarizer actually is. Do I have this right now?

If the gaps in the filer are vertical, then a horizontal magnetic field would be able to pass through that filter, is that correct?

Is it because of the way electrons in the filter can move? In a vertical filter the electrons can move up & down but not back and forth, which allows for a vertical electric field & horizontal magnetic field but not the reverse.

At first I was thinking the electric field was simply passing through the gaps in the filter and that it could pass through since the gaps & the field were oriented the same way. But now I think that's incorrect.

 

[haruspex]

Thank you for the replies, everyone! After reading your replies I think I had a misunderstanding of what a polarizer actually is. Do I have this right now?

If the gaps in the filer are vertical, then a horizontal magnetic field would be able to pass through that filter, is that correct?

Is it because of the way electrons in the filter can move? In a vertical filter the electrons can move up & down but not back and forth, which allows for a vertical electric field & horizontal magnetic field but not the reverse.

At first I was thinking the electric field was simply passing through the gaps in the filter and that it could pass through since the gaps & the field were oriented the same way. But now I think that's incorrect.

No, you have it backwards.
If the electric field is aligned with the wires then it is unable to generate an oscillation in the potential. The wires screen space beyond the filter from the field. Instead, electrons oscillate in the wires so as to neutralise the changes in the potential.

You can think of the oscillating electrons as generating a new wave in both directions. In the forward direction it is completely out of phase with the original field, cancelling it.

This is analogous to a sound wave in a tube. If it hits a closed end, the oscillation of the air molecules is inhibited, producing a reflection; at an open end, the oscillation of the pressure is inhibited, again producing a reflection.

 

[flintstones]

Ok, I think I kind of get it. What I'm confused about now is the orientation of the wires in a vertical polarizer.

In the image I put in my first post, it looks like the wires and the electric field are parallel and yet the wave makes it through, which is the opposite of what you're saying.

In a vertical polarizer are the wires aligned horizontally then? That seems wrong... I am missing something here.

 

[haruspex]

Ok, I think I kind of get it. What I'm confused about now is the orientation of the wires in a vertical polarizer.

In the image I put in my first post, it looks like the wires and the electric field are parallel and yet the wave makes it through, which is the opposite of what you're saying.

In a vertical polarizer are the wires aligned horizontally then? That seems wrong... I am missing something here.

The diagram in post #1 can be taken as schematic rather than literal. Besides, it need not be a wire grid, and I'm unsure how other filters work.
See the diagram at https://en.m.wikipedia.org/wiki/Polarizer#/media/File:Wire-grid-polarizer.svg

 

[rude man]

Simply: a polazier polarizes the electric field, not the magnetic field. The magnetic field might as well not be there as far as the polarizer is concerned.