Light waves through polarizers: transverse or longitudinal?

[Rtenhoor]

A question about the light-waves and the double-slit experiment:
Light can be polarized: If you turn a polarization sheet in a polarized beam of light, you can see that polarized light has an angle. So the light-wave is transverse (right?)

But how does a transverse wave ‘bend’ as it goes through the slits?
(it went straight ahead before it arrived at the slits…)

 

[BvU]

Hello R,

But how does a transverse wave ‘bend’ as it goes through the slits?

Huijgens principle. Actually, it diffracts (fraunhofer)

it went straight ahead before it arrived at the slits…

You sure ? Or are you only looking at the 'it's that do go straight ahead ?

 

[Rtenhoor]

Many thanks for the answer. The wikis seem to be about longitudinal waves.
However, light is not a longitudinal wave, because longitudinal waves cannot be polarized but light-beams can.

According to Maxwell/Feynman a light probability wave is actually 2 waves in two fields: electro & magnetic.
Feynman (I believe) added a complex component to the light-probability-wave: so the wave moves in a 'complex' field?
I do not understand this, as complex numbers do not actually exist in the real-world...

 

[Ibix]

Many thanks for the answer. The wikis seem to be about longitudinal waves.

No - both Huygens' Principle and Fraunhofer diffraction are applicable to light. Both the links BvU provided explicitly mention optics, so that should be clear.

According to Maxwell/Feynman a light probability wave is actually 2 waves in two fields: electro & magnetic.

According to a relativistic interpretation of Maxwell's equations, light is an oscillating electromagnetic field - the electric component oscillates in one direction and the magnetic in the perpendicular direction, but it's the same field. There's no probability in this model - it's purely classical.

Feynman (I believe) added a complex component to the light-probability-wave: so the wave moves in a 'complex' field?
I do not understand this, as complex numbers do not actually exist in the real-world...

I know enough about the quantum theory of light to know it's really complicated. It does make heavy use of complex numbers, yes, so you may need to adjust your intuition about whether or not complex numbers really exist.

 

[Rtenhoor]

In the wiki it says: '...propagates from that region in all geodesic directions'. They do seem to be talking about longitudinal waves...
I understand the mathematics are working, but how can longitudinal waves be polarized? (i.e. have an angle)
Is it possible to polarize a sound-wave?

 

[jbriggs444]

In the wiki it says: '...propagates from that region in all geodesic directions'. They do seem to be talking about longitudinal waves...

How does "propagate in all directions" imply longitudinal waves?

 

[Rtenhoor]

That's by imagination, I guess: it moves out in the shape of a ball(?). Can a transverse wave do that at all?

 

[jbriggs444]

That's by imagination, I guess: it moves out in the shape of a ball(?). Can a transverse wave do that at all?

Why not? Every incremental [nearly] planar segment of a spherical wavefront can be transverse.

For example in the 2 dimensional case, a stone dropped into a pond produces a transverse wave in every direction.

 

[Rtenhoor]

That's an interesting thought. I think you are right. Many thanks to all for the answers!

I am trying to imagine how the individual segments of the wavefront would move in the case of a transverse wave propagating away from the centre.
I guess there could be a ring-shaped transverse wavefront. (A sphere-shaped wavefront I cannot easily imagine: the poles of the sphere would need to be at stand-still, it appears) If the ring was very large, the [nearly] planar segments' transverse movement would also cause a longitudinal wave propagating sideways.

So, a transverse wave would diffract in the same way as a longitudinal wave?
What if it was polarized in some direction, would that influence the double slit experiment?

In the 2 dimensional example, the wave would move in the 3rd dimension.
To any 2 dimensionally limited observer, the wave would appear longitudinal. Or am I mistaken?

 

[Ibix]

I appear to have missed a few posts - apologies.

I am trying to imagine how the individual segments of the wavefront would move in the case of a transverse wave propagating away from the centre.

Nothing moves in an electromagnetic wave. The direction of the electric field at a point changes sinusoidally, and always points perpendicular to the propagation direction of the wave. But there are no little bits of electromagnetic field waving up and down.

A sphere-shaped wavefront I cannot easily imagine: the poles of the sphere would need to be at stand-still, it appears

If the wave is coherent, this is true. But things that emit coherent radiation emit zero strength in the polar direction. Non-coherent radiation can go in all directions because there's no particular phase or polarisation relationship to break down.

So, a transverse wave would diffract in the same way as a longitudinal wave?

Both transverse and longitudinal waves diffract according to the same basic maths. I don't know that they diffract exactly the same - you'd have to find some phenomenon that supported both longitudinal and transverse modes at the same speed to compare sensibly. I can't think of one off the top of my head.

What if it was polarized in some direction, would that influence the double slit experiment?

I believe so - there's no way for two differently polarised waves to exactly cancel.

In the 2 dimensional example, the wave would move in the 3rd dimension.
To any 2 dimensionally limited observer, the wave would appear longitudinal. Or am I mistaken?

See above - electromagnetic waves are not mechanical waves.

 

[Rtenhoor]

Nothing moves in an electromagnetic wave. The direction of the electric field at a point changes sinusoidally, and always points perpendicular to the propagation direction of the wave. But there are no little bits of electromagnetic field waving up and down.

See above - electromagnetic waves are not mechanical waves.

Thanks! I suppose the main difference between a mathematical wave of nothingness and a wave in some medium is that the mathematical wave has no push-back from other particles. However, an oscillation does (in my mind) give a clue that there is a push-back: the further off-centre a particle moves, the harder it will be pushed back by other particles, leading to an oscillation (and wave).
What would cause an oscillation in a mathematical, electromagnetic wave?

 

[Nugatory]

What would cause an oscillation in a mathematical, electromagnetic wave?

In an electromagnetic wave it's the interaction between the magnetic and electrical fields. A falling magnetic field causes an increasing electrical field and vice versa, so as one falls to zero it pushes the other to a peak and back again.

This is properly described by solving Maxwell's equations; you'll find many good derivations if you google for "Maxwell wave equation".

 

[Rtenhoor]

In an electromagnetic wave it's the interaction between the magnetic and electrical fields. A falling magnetic field causes an increasing electrical field and vice versa, so as one falls to zero it pushes the other to a peak and back again.

This is properly described by solving Maxwell's equations; you'll find many good derivations if you google for "Maxwell wave equation".

That's interesting! I wonder if you know of an explanation of the way the interaction works?

 

[Ibix]

That's interesting! I wonder if you know of an explanation of the way the interaction works?

Maxwell's equations, in short. The derivation of the wave equation from them is about four lines if you know any vector calculus.

A rough overview is that a changing magnetic field induces an electric field and a changing electric field induces a magnetic field. So the magnetic part of the wave acts like a restoring force for the electric part and vice versa.

 

[Rtenhoor]

Maxwell's equations, in short. The derivation of the wave equation from them is about four lines if you know any vector calculus.

A rough overview is that a changing magnetic field induces an electric field and a changing electric field induces a magnetic field. So the magnetic part of the wave acts like a restoring force for the electric part and vice versa.

Sorry, not the maths... I am just curious what is meant by the word 'induces' (or 'acts like' or even 'force' for that matter)...

 

[Nugatory]

I am just curious what is meant by the word 'induces' (or 'acts like' or even 'force' for that matter)...

"Induces" literally means "leads to". It is a simple observational fact that when an electrical field is changed the magnetic field at that point will also change with it, so we say that changes in one field "induce" a change in the other.

Waves that involve something physical moving back and forth (sound waves in air, ripples on the surface of a body of water) all work in the same general way: displacing whatever is waving causes some force that pushes it back towards its original position. For example, water ripples involve the surface of the water rising up while gravity is pulling it back down; sound waves involve air moving sideways, compressing the nearby air causing the pressure that pushes the moving air back where it came from. In all wave problems, we call this the "restoring force" and all waves obey the same differential equation - called the "wave equation" and Google is your friend here - relating the restoring force to the frequency, amplitude, and speed of the waves.

Although nothing is physically waving back and forth, it turns out that strengths of the electrical and magnetic fields are related in the same way (and as @Ibix says, you can get from Maxwell's equations to the wave equation in four lines). That's where "acts like" comes from - everything you learn from solving the math for one problem carries over to the other one.

Sorry, not the maths...

Fair enough, as long as you are aware that without the math everything we're saying is just handwaving, and nowhere near precise enough to use as a base for deeper understanding.

 

[Ibix]

There's not a lot to add to what @Nugatory said. The problem when you study science is the same as when a child asks why? Why? Why? Eventually the answer is just "because that's the way it is - we have no deeper explanation".

There's no deeper classical explanation for light than "when the electric field changes, the magnetic field also changes, and this happens to conspire to allow a propagating wave". There's a much more precise answer, which is Maxwell's equations. Which say what I just said but with predictive power.

You can get into quantum theory, but all that adds is some funny stuff when light intensity is low. What is a photon? A propagating excitation of the (quantised) electromagnetic field. Light is one or more of them. Again, there's a precise mathematical statement of that (or so I am told - quantum field theory is on my to-do list), but no deeper answer.

 

[Rtenhoor]

Many thanks for everybody's time and answers! I learned a lot.
There are many different waveforms possible (especially in a 3 dim or even 4 dim field) and different waves have to behave according to different mathematical rules.