Mechanical Universe The Great Polaroid Lens Experiment

krd

This has been kind of bothering me.

It's an experiment demonstrated at the end of one of the episodes of the Mechanical Universe.

1. A light beam is projected onto a screen.

2. Two polaroid sheets are placed in the beams path, where the grating of the sheets are at a 90 degree angle to each other. This blocks the beam.

3. A third polaroid sheet is place between the two other sheets - the grating is tilted at a 45 degree angle to the grating on the other two sheets. And amazingly, like black magic, light passes to the screen.

It doesn't make sense to me, why that should happen. To me it looks like a glitch in reality.

What is happening to the light beam to allow the middle sheet to change the angle the light is polarised in?

pvt6zh395dqbrj

Hi,

The intensity of transmitted light through a polariser is given by I=I0Cos^2(theta)

where I is the transmitted intensity, I0 is the initial intensity and theta is the angle between the grating of the polariser and the polarisation vector of the initial light beam.


So, lets for argument sake say that the beam is initially polarised in the same way as the first polariser when it comes out of the light source.

The transmission through the first polariser is then I1=I0Cos^2(0) = I0. so all the light gets through the first polariser.

The second polariser is now at 90 degrees so I2=I1Cos^2(90) = I0Cos^2(90) = 0. So none of the light gets through.

Now lets imagine we place a third polariser between the first and second at 45degrees.

The transmission through the first polariser is the same I1=I0.

Now for the middle polariser...whcih I'll call the second polariser.

I2=I1Cos^2(45)=I0/2.

This beam is now polarised at 45 degrees to the first polariser. Which means that the angle between its polarisation vector and the last polariser is now 45 degrees also.

I3=I2Cos^2(45)=I2/2=I0/4.

So if you have three polarisers in steps of 45 degrees, you get 1/4 the light intensity out.

krd

Harlan Weak Archivist wrote: »

I3=I2Cos^2(45)=I2/2=I0/4.

So if you have three polarisers in steps of 45 degrees, you get 1/4 the light intensity out.

Yeah, I came across that explanation and formula, in my travels for answer.

I understand that explanation - but I'm still bothered.

Where I still have a problem. Or really what my problem is, is more to do with what I imagine is happening to the light as it travels through each sheet. This could be down to me having a misconceptions about light. It could be how I'm conceiving light in the first place.

What I imagine to be happening: When the light beam starts at the projector, it's made up of waves oscillating in all directions.

And how I understand a polarising sheet to work - is the dark strands of polymer, extinguish the light that is not oscillating in the plane of the grating. The polymer strands absorb it. As far as I am aware, it's gone. (I know some light that's not perfectly in the plane will pass too - I'm not really sure by what mechanism - giving probability as explanation doesn't really tell me what mechanism is causing some light to pass and others to not - I think it has to do with what point in the cycle the wave is at when it reaches the grating - some light fudges it's way through)

The transmission through the first polariser is then I1=I0Cos^2(0) = I0. so all the light gets through the first polariser.

That statement doesn't really make sense to me. As far as I am aware, the light in outside the plane of the grating is gone - extinguished. So, all the light is not getting through the first polariser.

As I understand it, the light outside the plane of the polariser is extinguished.

Put a second polaroid sheet at a 90 degree angle to the first one, and all the light is extinguished.

What's really baffling to me, is by placing a third polariser at 45 degrees between the other two, it seems to un-extinguish part of the light.

Or that the action of the polariser is to twist the plane of the light, instead of extinguishing light not in its' plane.

In fact, I would expect by putting the third polariser between the other two, even more light should be extinguished.

The intensity equation (I=I0Cos^2(theta)) doesn't recognise polarity as I understand it.

pvt6zh395dqbrj

Hi,

"That statement doesn't really make sense to me. As far as I am aware, the light in outside the plane of the grating is gone - extinguished. So, all the light is not getting through the first polariser."

I said near the start of my last post that I was going to assume the light was polarised in the plane of the first polariser, meaning all the waves were oscillating in the same direction. The argument is the same if its un-polarised (all the waves in different directions).

"The intensity equation (I=I0Cos^2(theta)) doesn't recognise polarity as I understand it."

It does. This equation is essentially the dot product between two vectors - the polarisation vector of the light wave and the vector that describes the direction of the polariser.

A polariser works like this:

Imagine a wire grid. A square of wire that has wires running from the top to the bottom all across - like an egg flip, but the wires are really thin.

Imagine a single light wave, oscillating up and down in the direction that the wires run. This light wave will cause the electrons in the wires to move up and down also and the wave will be absorbed. It will not pass through the polariser.

Now imagine a single light wave oscillating up and down perpendicular to the direction of the wires. The wave in this case doesn't cause the electrons to move (because the wire is really thin and cant move in that direction) so the light wave passes through.

so already we have the situation that the polariser will completely extinguish light in one direction, and pass light in another.

Now imagine a single light wave oscillating somewhere in between. Lets say 45 degrees to the direction of the wires. You can imagine that this wave will push the electrons in the wire up and down (and hence be absorbed) but not as much as in the case where the wave in parrallel to the wires.

you can show that the amount transmitted will be equal to the dot product of the light wave (which has magnitude Io and direction whichever way the light waves are oscillating), and the vector describing the polariser (which has a magnitude of one and is in the direction of the wires).

From this we have the equation known as Malus' Law:

I=Iocos^2(theta).

the transmitted wave will always have a direction perpendicular to the wires and a magnitude given by the above equation.

For visible light, its the same but scaled down. The important things to note are that the polariser will transmit a percentage of the light depending on the angle between the light wave and the polariser.

An un polarised light source is just a bunch of waves all oscilating in different directions (lets again for arguments sake say that the polarisation of any individual light wave doesn't change with time).

The amount of transmitted light intensity will just be the addition of the dot products of all the individual light waves with the vector that describes the direction of the polariser.

So now, if I place two of these wire grids one after the other, and the wires are perpendicular to each other, its clear that none of the light will get past both polarisers.

The light that passes through the first polariser will become polarised in one direction, then this will get blocked by the second polariser.

But if I have three polarisers - one with the wires straight up/down, the second with the wires at 45deg to the first, and the last with the wires running left/right -

Well then the light that passes by the first polaiser will be oscillating left/right.

This then passes through the second polariser - after which it starts to oscillate at 45 degrees to what it was.

Then it meets the third polariser. The angle between the light and the polariser is now 45 deg, so some of the light gets through.

krd

Harlan Weak Archivist wrote: »

A polariser works like this:

Imagine a wire grid. A square of wire that has wires running from the top to the bottom all across - like an egg flip, but the wires are really thin.

Imagine a single light wave, oscillating up and down in the direction that the wires run. This light wave will cause the electrons in the wires to move up and down also and the wave will be absorbed. It will not pass through the polariser.

This is how I understood polariser to work.

It's subtraction - there's no magic twisting going on.

Malus' Law:

I=Iocos^2(theta).

the transmitted wave will always have a direction perpendicular to the wires and a magnitude given by the above equation.

No, the light with the maximum intensity will be the light with a polarity in the same plane as the wires. Light polarised with an angle off will diminish in intensity as the angle increases. By 45 degrees the intensity is 50% of the maximum, by 90 degrees, it's 0% of the maximum - it's extinguished. That's just with a single sheet. If a polariser only transmitted light in the same plane as the wires, it would pass very little light.

Light that is off angle and is transmitted, is due to the probability, that it's wave will be at the right shape in it's cycle, to fudge its's way through the grating - the greater the angle, the lower the probability it will be the right shape to get through - I could be completely wrong here, but that's my understanding of the light wave.


If you put an infinite number of polariser in series, with each successive stage, you'd lose more light that's off the angle of the wires. In theory, light that is polarised at theta, will continue to pass through. You can see that by looking at Malus' Law.

If you put two polarisers in series, one where the angle is 90. You don't get complete darkness. Light from the original source, that was neither polarised at 0 or 90 degree angle will pass through. I might be wrong in this calculation - light at 45 degrees will be at 0.25 of its' intensity at the source.

I'm not saying Malus' equation is wrong. But since polarisation is caused by subtracting light, the order of the polarising sheets shouldn't make a difference - but in reality it does.

The whole thing really bothers me. It's like a glitch in a computer game.

Well then the light that passes by the first polaiser will be oscillating left/right.

This then passes through the second polariser - after which it starts to oscillate at 45 degrees to what it was.

This is where I have a problem. When you say the wave starts to oscillate at 45 degrees, from what I understand of what you're saying, the wave has been twisted to oscillate at 45 degrees. And this contradicts my understanding of polarisation as being a subtractive process.

pvt6zh395dqbrj

"No, the light with the maximum intensity will be the light with a polarity in the same plane as the wires. "

Perhaps we speak of different things when we talk of the plane of the wires. I mean that the direction of the oscillation of the electric field of the light wave will be perpendicular to the direction that the wires run.

http://upload.wikimedia.org/wikipedia/commons/9/94/Wire-grid-polarizer.svg

"Light that is off angle and is transmitted, is due to the probability, that it's wave will be at the right shape in it's cycle, to fudge its's way through the grating - the greater the angle, the lower the probability it will be the right shape to get through - I could be completely wrong here, but that's my understanding of the light wave. "

I don't understand what "right shape it its cycle" mean but in general,
that's not a terrible way of looking at it. Every linear polarised wave, no matter its direction, can be thought of as the linear superposition of two orhtogonally polarised light fields. For convenience sake we might as well say that those two polarised fields are parrallel and perpendicular to the wires.

A light wave at 45 degrees to the wire is made up of a wave that is parrallel to the wires, which has half the intensity and gets absorbed. And a wave that is perpendicular to the wires and gets through - this also has half the intensity.

So the total amount that gets through is half the intensity at an angle that is perpendicular to the wires.

pvt6zh395dqbrj

"If you put two polarisers in series, one where the angle is 90. You don't get complete darkness. Light from the original source, that was neither polarised at 0 or 90 degree angle will pass through. I might be wrong in this calculation - light at 45 degrees will be at 0.25 of its' intensity at the source."

If you put two polarisers in series, at 90 degrees to each other, if they are perfect polarisers, you will get no light out at the end regardless of the original polarisation of the light source.

"I'm not saying Malus' equation is wrong. But since polarisation is caused by subtracting light, the order of the polarising sheets shouldn't make a difference - but in reality it does. "

It isn't wrong. Polarisation is not caused by subtracting light. Its caused by the absorption/transmission of light depending on the direction its electric field is oscillating (the simplest polarisers work by absorption/transmission but there are fancier kinds).

Malus' Law predicts that the order of the sheets will make a difference. It predicts that if I have three polarisers with angles (0 90 45) then I'll get no light through. But if I place them (0 45 90) then I get a quarter of my intensity through.

krd

Thanks for all your responses.

I'm going to have a think about it - and go away read more stuff.

I *embarrassed cough* studied some physics at third level. I didn't have great ground work (awful secondary school). And for various reasons, I built up a lot of confusing misconceptions - partially down to oversimplified and incorrect explanations - and me filling in the gaps. I could busk my way through exam questions, without really understanding the underlying theory. But that was in the days before google, and all you had was your lecture notes and the library wasn't that hot. Outside of the universities the libraries were a joke. Kids these days are spoiled. I once had to take an epic bus journey to look at a single page, in single book.

Harlan Weak Archivist wrote: »

"No, the light with the maximum intensity will be the light with a polarity in the same plane as the wires. "

Perhaps we speak of different things when we talk of the plane of the wires. I mean that the direction of the oscillation of the electric field of the light wave will be perpendicular to the direction that the wires run.

This is something I have to look into.

Just a quick question? Does the magnetic field of the light wave pass through the polariser without being absorbed by the electrons.

And a more general question: Is it only the electric field of the light wave that interacts with electrons (is absorbed by electrons).

I'm slowly piecing things together. Does the electron have a magnetic field perpendicular to its electric field? And does the light wave's magnetic field interact with with this field?

"Light that is off angle and is transmitted, is due to the probability, that it's wave will be at the right shape in it's cycle, to fudge its's way through the grating - the greater the angle, the lower the probability it will be the right shape to get through - I could be completely wrong here, but that's my understanding of the light wave. "

I don't understand what "right shape it its cycle" mean but in general,
that's not a terrible way of looking at it.

Ah, haw....."the right shape in its cycle".....When I was searching the interweb looking for answers - and didn't know precisely what I was looking for. I came across two lectures on Youtube. One in Spanish and the other in Hindi. I neither read, write, or speak, Spanish or Hindi - so I had to make a few guesses about what they were on about.

Every linear polarised wave, no matter its direction, can be thought of as the linear superposition of two orhtogonally polarised light fields. For convenience sake we might as well say that those two polarised fields are parrallel and perpendicular to the wires.

I'm kind of chipping away at some of those concepts - you couldn't recommend a book? (well written - doesn't have to "accessible") I find the more I read, even if it's a retelling of the same stories, I get one more little piece of the puzzle.

A light wave at 45 degrees to the wire is made up of a wave that is parrallel to the wires, which has half the intensity and gets absorbed. And a wave that is perpendicular to the wires and gets through - this also has half the intensity.

So the total amount that gets through is half the intensity at an angle that is perpendicular to the wires.

What are those waves called? I forgotten a lot of stuff - I'm trying to remember what ordinary rays, and extradionary waves are - I'm trying to jog my memory on a lot of stuff - stuff I never really understood in the first place.

Again, thanks for all your responses.

pvt6zh395dqbrj

"Just a quick question? Does the magnetic field of the light wave pass through the polariser without being absorbed by the electrons.

And a more general question: Is it only the electric field of the light wave that interacts with electrons (is absorbed by electrons)."

In general the magnetic component of a light wave will be smaller the the electric field by a factor of c. So in almost all cases it can be ignore - except in the case of very high intensity light.

The picture I told of the wave causing the electrons to move up and down and absorbing the wave was a conceptual idea that's not a million miles away from the complete picture, but it is certainly not the full story. As you say, one must consider the magnetic field also.

What actually happens to the electric and magnetic fields of the light wave at the interface between the air (or whatever the wave is moving in) and the wire grid is the result of how maxwell's laws behave in conducting media. Its beyond the scope of the model that we are currently talking about.

I guess, to just sweep the problem of the magnetic field under the rug, we can say that the electric field will always have an accompanying magnetic field that is orthogonal to it and smaller in magnitude by a factor c.

" Does the electron have a magnetic field perpendicular to its electric field? And does the light wave's magnetic field interact with with this field?"

An electron that is stationary will have no magnetic field. Magnetic fields come from moving electrons. The magnetic field of a moving electron is quite complicated but it is well known and it depends on how fast the electron is moving, accelerating and so on. Really though, the original problem of the three polarisers and the light wave can be fully described without considering this.

"What are those waves called? I forgotten a lot of stuff - I'm trying to remember what ordinary rays, and extradionary waves are - I'm trying to jog my memory on a lot of stuff - stuff I never really understood in the first place.

Again, thanks for all your responses."

The waves I was talking about are just arbitrary waves with no names. I was just talking conceptually. Ordinary Waves and Extraordinary waves are different things. They are the names given to waves that are in birefringent material. A polariser can sometimes be birefingent and use the extra ordinary and ordinary waves to control the polarisation of a wave - but this is not what I spoke of in my last post (although its quite analagous in alot of ways. )

Walter Lewin is a very good teacher and his lectures are on youtube, but you might need to stick with it a while before he gets to Malus' Law - i think its 30 lectures or so before he talks about it.

You could try this:

http://motionmountain.net/index.html

I'll try to find some other internet resources that may be useful, but if you are looking for a good optics book - Hecht is quite good.

krd

Harlan Weak Archivist wrote: »

The picture I told of the wave causing the electrons to move up and down and absorbing the wave was a conceptual idea that's not a million miles away from the complete picture, but it is certainly not the full story. As you say, one must consider the magnetic field also.

I was familiar with how excited electrons released photons. I never really got around to understanding how electrons absorbed photons.

But things are confusing - like trying to reconcile Niels Bohr's ideas on light emission, from what I know....And free electrons in a plasma - to tell you the truth, I don't really know what's happening.

What actually happens to the electric and magnetic fields of the light wave at the interface between the air (or whatever the wave is moving in) and the wire grid is the result of how maxwell's laws behave in conducting media. Its beyond the scope of the model that we are currently talking about.

Thanks, I'll look into that ....now I know a little more of where to go to expand my conceptual model. (Which at the minute is bits of blue tack, and odd piece of lego, and some string)

I also assumed, that light travelling through air over a short distance, is mostly travelling through vacuum - and the waves that collide with gas molecules in the air could be discounted.

As far as I am aware, polarization in a vacuum shouldn't be any different to polarization in air over short distances.

An electron that is stationary will have no magnetic field. Magnetic fields come from moving electrons. The magnetic field of a moving electron is quite complicated but it is well known and it depends on how fast the electron is moving, accelerating and so on. Really though, the original problem of the three polarisers and the light wave can be fully described without considering this.

My concept of the electron is very confused too. Like the time I thought I understood it - then in a conversation with my lecturer, he said electrons in a conducting material never leave the orbit of their atom. And I asked him what he meant and he was kind of jaded and said "all you'll pick it up" and I didn't

I read Jim Baggotts The Meaning of Quantum Theory, over Christmas. There's a quote from Schrodinger on how he wished he'd never had anything to do with quantum theory, as the free electron conflicted with his wave theory. And you know, I'm just as confused.

The waves I was talking about are just arbitrary waves with no names. I was just talking conceptually. Ordinary Waves and Extraordinary waves are different things. They are the names given to waves that are in birefringent material. A polariser can sometimes be birefingent and use the extra ordinary and ordinary waves to control the polarisation of a wave - but this is not what I spoke of in my last post (although its quite analagous in alot of ways. )

I'm trying to build a conceptual model in my own head of waves (light) which is tricky - as whenever I think I'm getting a grip on it, it slips through my fingers.

Walter Lewin is a very good teacher and his lectures are on youtube, but you might need to stick with it a while before he gets to Malus' Law - i think its 30 lectures or so before he talks about it.

I have no problem sitting through hours of lectures. I do need to revise my maths skills.

It's embarrassing how much basic stuff I've forgotten.

Malus' law looks fine to me. Where I had a problem with it, is it exposed my understanding of polarization to be incorrect. I do not understand properly how the light is transmitted. In my head, I was trying to marry an idea of shadows, with my understanding of transverse waves.

Sound waves...They are beautiful in their simplicity by comparison. But when you think about them enough, they do throw up some horrible questions. Aw F- it...Maybe I don't understand them either.

Again, thanks.