Why Does Light Reemerge with a Third Polarizer?

[2112rush2112]

Cross two polarizers and all light is blocked. Inserting a third polarizer in between two crossed polarizers and light again reemerges from the polarizers. Why is this? I'm trying to wrap my mind around this.

I noticed that certain transparent plastics (cellophane, e.g.,) also allow some light to pass through the crossed polarizers because the plastic acts as a sort of 1/2 wave plate. Could it be that the third polarizer is also acting as a 1/2 wave plate, allowing light to transmit through the crossed polarizers?

Again, how can light be transmitted through crossed polarizers when a third polarizer is introduced in between the crossed polarizers?

 

[G01]

The easiest way to think about this polarizer experiment is in terms of vector projections.

The first polarizer allows only the component of the E-Field parallel to the polarizer axis through to the other side. Call this direction the 'x-axis.' The second polarizer is rotated 90degrees relative to the first. Thus, only the component of the light's E-Field parallel to the 'y-axis' will get through.

Since the first polarizer forces the light to be polarized along the x-axis, the light's field has no projection along y. Thus, no light gets through the second polarizer.

When we add a third polarizer at, say, a 45 degree angle relative to the first (call this the x'-direction) and in between the first two polarizers, the situation changes. After the first polarizer, the light is still polarized along the x-axis. Next, the light hits the new polarizer, which only allows a component of the light parallel to the x'-axis through. Light polarized along the x-axis does have a projection along the x' axis. Therefore some light gets through, polarized along x'.

When the x' polarized light hits the last polarizer some now get's through, because light polarized along x' has a projection along the y direction, unlike light polarized along x.

This is hard to explain without pictures. For some more info check out:

http://web.physics.ucsb.edu/~lectur...s/Crossed polarizers with third polarizer.htm

 

[tiny-tim]

welcome to pf!

hi 2112rush2112! welcome to pf!

i suspect you're comparing polarizers with colour filters

if you have a red filter and a green filter, nothing will pass through both filters, and if you put another filter between them, it makes no difference

this is because a colour filter doesn't change anything … it may block out some light, but any light that does get through is unchanged

a polarizer, however, does change the light that gets through

 

[2112rush2112]

The easiest way to think about this polarizer experiment is in terms of vector projections.

The first polarizer allows only the component of the E-Field parallel to the polarizer axis through to the other side. Call this direction the 'x-axis.' The second polarizer is rotated 90degrees relative to the first. Thus, only the component of the light's E-Field parallel to the 'y-axis' will get through.

Since the first polarizer forces the light to be polarized along the x-axis, the light's field has no projection along y. Thus, no light gets through the second polarizer.

When we add a third polarizer at, say, a 45 degree angle relative to the first (call this the x'-direction) and in between the first two polarizers, the situation changes. After the first polarizer, the light is still polarized along the x-axis. Next, the light hits the new polarizer, which only allows a component of the light parallel to the x'-axis through. Light polarized along the x-axis does have a projection along the x' axis. Therefore some light gets through, polarized along x'.

When the x' polarized light hits the last polarizer some now get's through, because light polarized along x' has a projection along the y direction, unlike light polarized along x.

This is hard to explain without pictures. For some more info check out:

http://web.physics.ucsb.edu/~lectur...s/Crossed polarizers with third polarizer.htm

Thanks for your answer. But I'm still confused. I take it that the x' axis is 45 degrees from the x axis, and thus the second polarizer is rotated 45 degrees from the first, no?

And if it is, then it would make sense that the x' polarizer (the polarizer we sandwiched in between the crossed polarizers) would transmit 1/2 the light that fell on it from the first, "x" polarizer (you called this, "x' polarized light").
And since the 'x' polarized light' is rotated 45 degrees from the y polarizer (the last polarizer in the system), then the y polarizer will pass 1/2 of the light from the x' polarizer. Is this correct?

You also said, "Since the first polarizer forces the light to be polarized along the x-axis..." I thought polarizers were passive devices; devices that can't "force" anything, but passively allows certain components (x or y components) to pass through, no?

 

[G01]

Thanks for your answer. But I'm still confused. I take it that the x' axis is 45 degrees from the x axis, and thus the second polarizer is rotated 45 degrees from the first, no?

Yes, this is correct.

And if it is, then it would make sense that the x' polarizer (the polarizer we sandwiched in between the crossed polarizers) would transmit 1/2 the light that fell on it from the first, "x" polarizer (you called this, "x' polarized light").

Correct. Also, if the angle was not at 45 degrees , but some other angle between 0 and 90 degrees, the ratio of transmitted light to non-transmitted light would not be 50/50, but would depend on the magnitude of the projections from the x-axis onto the x'-axis. Malus' Law is the mathematical statement of this idea: http://en.wikipedia.org/wiki/Law_of_Malus#Malus.27_law_and_other_properties

And since the 'x' polarized light' is rotated 45 degrees from the y polarizer (the last polarizer in the system), then the y polarizer will pass 1/2 of the light from the x' polarizer. Is this correct?

Yep.

You also said, "Since the first polarizer forces the light to be polarized along the x-axis..." I thought polarizers were passive devices; devices that can't "force" anything, but passively allows certain components (x or y components) to pass through, no?

Of course, you are correct. The polarizer is a passive device. I took some "poetic license" with my choice of language.

 

[Khashishi]

However, the polarizers do modify the state of the photons passing through, so it's not entirely passive. The polarizer acts as a measurement device, and you cannot measure something without changing it. That's why adding a second polarizer can increase the transmission through the third polarizer.

 

[G01]

However, the polarizers do modify the state of the photons passing through, so it's not entirely passive. The polarizer acts as a measurement device, and you cannot measure something without changing it. That's why adding a second polarizer can increase the transmission through the third polarizer.

You are using the terms passive and active in a confusing manner given the problem.

Rush is using passive and active in the engineering sense, which makes sense in this context. A passive device is one that doesn't require energy input from to function. An active device is one that does require energy input to function.

In this sense, both a lossy optical medium (one that absorbs light) and a gain medium inside a laser (amplifies light) alter light by absorbing and emitting photons, but the first is "passive" and the second is "active."

 

[2112rush2112]

Yes, this is correct.
Correct. Also, if the angle was not at 45 degrees , but some other angle between 0 and 90 degrees, the ratio of transmitted light to non-transmitted light would not be 50/50, but would depend on the magnitude of the projections from the x-axis onto the x'-axis. Malus' Law is the mathematical statement of this idea: http://en.wikipedia.org/wiki/Law_of_Malus#Malus.27_law_and_other_properties
Yep.
Of course, you are correct. The polarizer is a passive device. I took some "poetic license" with my choice of language.

And now for the Grand Finale: The second polarizer (x' polarizer) transmits 1/2 the light that was passed through the first polarizer. In turn, the third polarizer (the y polarizer) passes 1/2 the light that had been passed by the second polarizer. We see, on our movie screen, 1/4 the light that had been emitted by the initial light source (In fact, I may summarize this idea in an ad-hoc law, and the Law states: "A polarizer will pass light in one plane of polarization, block light in its orthogonal plane of polarization, and pass or block photons in-between these two planes of polarization." Do you agree with this ad-hoc law?).

What we are seeing therefore, and pardon my redundancy, is one-fourth the number of photons on the movie screen that originated from the initial light source. This one-fourth composition of photons consists of not (emphasis added) linearly-polarized photons in the x-plane, nor linearly-polarized photons in the y-plane. Rather, we see the photons on the movie screen that were somewhere in-between the x-plane and y-plane (the x-plane photons were blocked by the y-polarizer and the y-photons were blocked by the x-polarizer. The photons in-between ultimately made their way to the movie screen as a spot of light). For rhetoric's sake, I'll refer to these photons as the "in-between photons"--photons that were neither polarized in the x-plane nor the y-plane, but somewhere "in between" the x and the y.

An 'in-between' photon, from our previous posts on this thread, has a 50/50 chance of passing through a second polarizer that's rotated at 45 degrees from the first, then a 50/50 chance of being passed through the third polarizer. Suppose we consider only the 'in-between' photon that passed through all three polarizers. The second polarizer did nothing to the photon; the photon merely passed straight through it! And at the end of the day a photon successfully navigated crossed polarizers. <sigh>

To crystallize my thought: The first polarizer will pass some in-between photons emitted by a light source. By the aforementioned 'law', any polarizer orthogonal to the first must likewise pass some of the in-between photons. But we don't see this in nature; crossed polarizers do not pass any light from their native light source!

Can you see my problem here? Thank God this forum doesn't have an IQ requirement, otherwise I never would have made it past forum registration...

 

[2112rush2112]

The polarizer acts as a measurement device...

Sounds almost EPR-related. Or pulled from the Copenhagen Interpretation. Or extrapolated from Bell's Inequality violations. Or...

 

[sophiecentaur]

The stuff about movie screens would be OK if linear polarisation were used. Actually, to allow people to tilt their heads without messing up the picture, circular polarisations are used in stereo Cinema. Do you really want to talk about circularly polarised photons - or just stick with waves and fields, where the answer comes out with much more ease? Either model is valid.

 

[2112rush2112]

The stuff about movie screens would be OK if linear polarisation were used. Actually, to allow people to tilt their heads without messing up the picture, circular polarisations are used in stereo Cinema. Do you really want to talk about circularly polarised photons - or just stick with waves and fields, where the answer comes out with much more ease? Either model is valid.

Looks like I made a huge error in my use of the words "movie screen!" By "movie screen," I mean a screen where the light falls on after it exits the third polarizer. In college experiments, the Professor usually projects this light on what appears to be a small movie screen, hence my use of the word.

It was a bad idea for me to use it tho, since polarizers are used in actual stereoscopic cinema... :(

This discussion is confined to linear polarizers. And since a polarizer can pass photons that aren't entirely in the polarizer's axis (a polarizer that blocks x-axis photons can still pass photons that are in between the x-and y-axis), then why do crossed polarizers block 100% of light?

 

[G01]

And since a polarizer can pass photons that aren't entirely in the polarizer's axis (a polarizer that blocks x-axis photons can still pass photons that are in between the x-and y-axis), then why do crossed polarizers block 100% of light?

A polarizer does pass photons that are polarized at an angle in between the x and y axes, but the state of those photons is altered so that after passing through the polarizer, their polarization state is parallel to the polarizer.

sophiecentaur is right that you should stick to the wave model for light. You are confusing yourself by talking about photons. Polarizers can, of course, be described with a photon model of light, but doing so requires study of quantum mechanics and my guess is that you have not gotten there yet. One step at a time.

 

[sophiecentaur]

@ rush
OK - just avoiding the uninformed grabbing hold of the wrong end of the stick when they read what you wrote.

As you competently demonstrated, an explanation of polarisation in 'particle terms' is very convoluted, compared with one in which we just resolve field vectors. As both interpretations of EM are valid then why not go for the more straightforward explanation? People seem to feel the need to reach for 'photons' so often - as if it really implies a greater understanding. To my mind, it's like making love standing up in a hammock to do it that way

 

[G01]

People seem to feel the need to reach for 'photons' so often - as if it really implies a greater understanding. To my mind, it's like making love standing up in a hammock to do it that way

This is going on my physics quote list...

 

[2112rush2112]

...To my mind, it's like making love standing up in a hammock to do it that way...

Hey don't knock it till you try it.

 

[2112rush2112]

A polarizer does pass photons that are polarized at an angle in between the x and y axes, but the state of those photons is altered so that after passing through the polarizer, their polarization state is parallel to the polarizer.

sophiecentaur is right that you should stick to the wave model for light. You are confusing yourself by talking about photons. Polarizers can, of course, be described with a photon model of light, but doing so requires study of quantum mechanics and my guess is that you have not gotten there yet. One step at a time.

You said that "...the state of those photons is altered so that after passing through the polarizer, their polarization state is parallel to the polarizer." So it's the polarizer that's doing the altering to the photon, no? And if the polarizer is doing the altering, then indeed polarizers are active and not passive devices, no?

Sophiewcentaur, do you agree that the polarizer alters the orientation of some of the polarized light that passes through it? I thought polarizers just pass/block light.

...And if we want to discuss this with QM formalism, I'm hip with that. I don't see photons as sub-microscopic 'baseballs' being sent through the polarizers; no. They're probability amplitudes...

 

[sophiecentaur]

You said that "...the state of those photons is altered so that after passing through the polarizer, their polarization state is parallel to the polarizer." So it's the polarizer that's doing the altering to the photon, no? And if the polarizer is doing the altering, then indeed polarizers are active and not passive devices, no?

Sophiewcentaur, do you agree that the polarizer alters the orientation of some of the polarized light that passes through it? I thought polarizers just pass/block light.

...And if we want to discuss this with QM formalism, I'm hip with that. I don't see photons as sub-microscopic 'baseballs' being sent through the polarizers; no. They're probability amplitudes...

If what they did was as simple as all that - i.e. like a selective form of comb then what fraction of the power would be getting through? An infinitely small proportion.
I don't see much point in discussing the phenomenon in terms of photons but, in terms of E and H fields in the EM wave, a linear polariser selects the component of the field in one particular direction and rejects / absorbs components the other plane.
If you take plane polarised light and pass it through a plane polariser at 45 degrees then you will end up with a plane polarised wave with half power (1/(root two) amplitude) in the plane of the polariser. You 'could' say it had effectively altered the polarisation of the original wave but it has just selected a component of the E field. This new wave could, of course, be passed through a second polariser, at a further 45 degrees to the first which would then produce a wave with polarisation at right angles to the original wave and 1/4 power (1/2 amplitude). You could carry on doing this, losing half the poser each time you rotate the polarisation by 45 degrees.
People seem to think that this is, somehow, unthinkable and violates something fundamental. Why?

I think the notion of a polariser being "active" (something that was mentioned further up the thread) is nonsense because "active" implies a power source.

 

[sophiecentaur]

Hey don't knock it till you try it.

Did you not notice the bump on my head and the plaster cast on my leg?

 

[G01]

You said that "...the state of those photons is altered so that after passing through the polarizer, their polarization state is parallel to the polarizer." So it's the polarizer that's doing the altering to the photon, no? And if the polarizer is doing the altering, then indeed polarizers are active and not passive devices, no?

That is not what is meant by active and passive. As sophiecentaur said, being 'active' implies a power source. http://en.wikipedia.org/wiki/Passivity_(engineering)

 

[2112rush2112]

People seem to think that [polarizer action] is, somehow, unthinkable and violates something fundamental. Why?

I'm tellin' you bro, I have a PF Science Adviser (you) and a PF Gold Member and Homework Helper (G01) trying to explain this to me but it's still not sinking into my thick head! The polarizer is still kicking my ***!

If what they did was as simple as all that - i.e. like a selective form of comb then what fraction of the power would be getting through? An infinitely small proportion.

I understand this idea--the idea that a polarizer allows more light to pass than only and strictly those photons that pass in the polarizer's plane.

I don't see much point in discussing the phenomenon in terms of photons

Dr. David Goodstein of Mechanical Universe fame (remember that show?) tried to explain it quantum mechanically in an episode, but in doing so demonstrated that even Cal Tech faculty can be fallible.

You 'could' say it [the polarizer] effectively altered the polarisation of the original wave but it has just selected a component of the E field.

And here's where I run into difficulty. I'm trying to figure out how a polarizer can alter the polarization of light without being a half-wave plate. I thought only half-wave wave plates can do this (and even then, half-wave plates rotate light 90 degrees; not 45 degrees).

This new wave

So you do agree with G01 that polarizers do in fact alter photons in some way, correct? Not classicly, like a racemic mixture or glucose would, but an alteration of the photon's plane of polarization on a more fundamental level.

I would like to learn more about what happens to a photon as it exits a linear polarizer (Polaroid, Nicol prism, etc.). My first instinct is to learn about E and H fields, but that's all property of James Clerk Maxwell, and over 150 years old. Thus, to gain a better understanding of nature, it's best to look beyond Maxwell (as much as I do revere him), no?

 

[2112rush2112]

Did you not notice the bump on my head and the plaster cast on my leg?

Sh!t one hell of an orgasm....

 

[G01]

My first instinct is to learn about E and H fields, but that's all property of James Clerk Maxwell, and over 150 years old. Thus, to gain a better understanding of nature, it's best to look beyond Maxwell (as much as I do revere him), no?

Your first instinct is correct. The model that provides the better understanding is the one best suited to the problem. I agree with what sophiecentaur said earlier:

Do you really want to talk about circularly polarised photons - or just stick with waves and fields, where the answer comes out with much more ease? Either model is valid.

Emphasis mine. The problem can be understood in terms of photons, of course, but if you do not understand classical E and H fields yet, then focusing on photons is just going to make the physics of polarizers even more opaque. As all the physics of the problems is validly modeled with classical theory, you are not missing any of the physics by focusing on a classical picture for the time being.

 

[sophiecentaur]

My issue with trying to explain things in terms of photons is that they are not any more 'real' than fields. I can appreciate that it may be easier to have a picture of a little bullet traveling from A to B than some sort of nebulous set of invisible vectors out there (everywhere, in fact). The only thing we can measure, though, whatever we believe is happening between A and B, is the result, when we actually detect the energy. There are cases where the photon explanation fall out nicer and there are cases where the field explanation does it easier. There are also, say the two slits, where either model will give you an answer without too much trouble.

When you talk about getting a better understanding than Maxwell can give you, you need to be careful not to replace Maxwell with some more trivial model. The sort of photons that people use in these arm waving explanations are way more trivial than Maxwell. Any worthwhile photon model must include all the factors that Maxwell entails and then some. You can't replace Maxwell with something that's not as good and call that 'better understanding'.

The simplest form of polariser to consider is probably a dipole (or any straight wire) in an RF field. The classical way of treating it is to talk of the currents induced along the wire due, only to the component of the wave polarised parallel to the wire. and the re-radiation / reflection of energy in the form of waves that are polarised parallel to the dipole wire. The component of the incident wave normal to the wire is unaffected by it. All other polarisers do more or less the same thing; if it's happening in a solid then it's more complex but you could deal with that later. The polariser - because it is an object that is interacting with the wave - is a mechanism that 'measures' the states of the photons and resolves the uncertainty. When the photons have passed out of the other side, they are quantum objects again and could be anywhere, doing anything until they are measured again.

Applying photons to this. A photon has to have a certain energy so you can't have a 'component of a photon'. When the RF energy passes the wire, there is a probability that a certain proportion of the photons will interact with the wire. Surprise surprise, that probability just happens to correspond to half of the photons, when the incident wave is unpolarised (a random selection of radio signals from a massive selection of transmitters in all different orientations - that's like your ordinary light source). Moreover, if you are dealing with just one source (a linearly polarised signal), the probability of a photon interacting with the wire just happens to be proportional to the Cosine of the angle of orientation of the transmitting and receiving wires (the square of the E component). The good-ol' wave explanation predicts what will happen to the photons that we measure with our radio receiver. We can choose to believe that it was photons that jumped between the transmitter and receiver or we can say it was waves but, without putting another detector in the way (and messing up the experiment) we can't say which way it really happened. Those photons really have to have an instruction book with them to tell them how to behave like Mr Maxwell told them to and they can't ignore him.