# A light Interference doubt

I'm really confused about the way the light can suffer interference. I'll try to explain the way I think all this occurs and the question I have if this explanation was correct. I would like you guys to correct me if anything I say is wrong and to try to explain me the final question.

Light is a set of photons that oscilates creating an eletric and a magnetic field around them. When 2 photons are too close their eletric/magnetic fields can interact generating the interference. But this would need the 2 photons to be really close, doesn't? And this interference would occur only while the 2 photons were together. Like in the picture.

http://img13.imageshack.us/img13/5903/20573870.png [Broken]

Now look at the picture

http://img89.imageshack.us/img89/1899/skhgfshgdfgsdg.png [Broken]

Consider all light rays to be almost perpendicular to the surface. So the difference of luminous path would be 2d and, like all interference book says:

If 2d = (2n+1)/2 λ - constructive interference
If 2d = n λ - destructive interference

This is due to the phase inversion in B.

OK, BUT WHERE THE HELL DOES THE INTERFERENCE OCCURS?
B isn't in the same place than D, so the interference can't occur ON the surface. Does it occur in the human eye? How? Because I don't thinks the 2 rays will actually hits each other exactly IN the human eye.

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Light waves interfere with each other in the same manner as other types of waves. Go fill your bathtub and experiment with disturbing the smooth surface with different objects in different locations. Look at the interference patterns that occur.
Rays BE and DF are out of phase, so their amplitudes subtract. One is "pulling" while the the other is "pushing". Like two water waves encountering each other but one pushing water up while the other pushing the water down.

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Light waves interfere with each other in the same manner as other types of waves. Go fill your bathtub and experiment with disturbing the smooth surface with different objects in different locations. Look at the interference patterns that occur.
Rays BE and DF are out of phase, so their amplitudes subtract. One is "pulling" while the the other is "pushing". Like two water waves encountering each other but one pushing water up while the other pushing the water down.
I understand this push and pull interference. But the waves should be close (in other words, superposing) each other to interact, right? BE and DF aren't superposing each other. How can they interact? How can theey interfere?

Cthugha
BE and DF aren't superposing each other. How can they interact? How can theey interfere?
What makes you so sure these are not superposing? There are at least three ways to answer your question. I do not know which is best for your level of understanding, so I will try all three of them.

1) In the kind of drawing you show, you see straight light rays. If light were really only located on a small spatial scale, it would suffer badly from diffraction and spread quickly. That is why books typically tell that they assume plane waves for the kind of image you show. That means you have lots of such parallel beams next to each other. Therefore, there is also a parallel beam to A-B which ends at D and overlaps perfectly with the CD-Beam.

2) The lateral extent of any wave cannot be made arbitrarily small. The lower bound is roughly the wavelength of the light involved. In the picture you have shown, yon need a total path difference of lambda or 0.5 lambda for constructive or destructive interference. As most of the difference in path is covered by the vertical thickness of the thin film, the horizontal offset is significantly smaller than that and therefore typically much smaller than a wavelength. As the lateral extent of the wave is typically larger than the wavelength of the light, the two beams will indeed overlap pretty well.

3) The do-it-yourself-approach. Read up on the Huygens-Fresnel principle, which states that every point of the light wave serves as a source of a spherical wave, grab a pair of compasses and draw the whole interference scenario yourself. This will not help you at the moment, but is very instructive in the long run.

1) In the kind of drawing you show, you see straight light rays. If light were really only located on a small spatial scale, it would suffer badly from diffraction and spread quickly. That is why books typically tell that they assume plane waves for the kind of image you show. That means you have lots of such parallel beams next to each other. Therefore, there is also a parallel beam to A-B which ends at D and overlaps perfectly with the CD-Beam.

The light I've considered in the second image was a light source, not only a light beam (I've draw n a single ray just to make it easier to understand).
I've got your point now. Yes, there are many other rays can interact and "superpose" the AB ray. Part of my question is answered. BUt I still have some doubts.

Look at the following image (third image)

http://img716.imageshack.us/img716/1253/dfgdsfg.png [Broken]

In the second image we had that a ray parallel to AB that passes through D would superpose COMPLETELY DF. But that's because the surface was plane.

At third image we have that as the surface is not plane, the green ray cannot superpose completely the red one. They only intersect at B. The blue ray, eather. That way, the interference occurs only in a single point.

Now let's suppose an absurd thing for a moment (I know it's absurd but it is important for my understanding). If there was only the three beams drawed in the picture (no more light beam). For we to see the interference , should we put the eye exactly in A?

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Cthugha
For we to see the interference , should we put the eye exactly in A?
I suppose from a technical point of view, it would be much easier to put a screen there and watch the screen, but in principle yes. The interference will take place only at the positions where beams which are somewhat phase shifted with respect to each other actually have some spatial overlap.

Thanks Cthugha.

A final and last question.

For we to predict (mesure) where the interference will occur, we have that the light beams (emmited by the light source) have to be in phase immediatelly before the hit the surface. How can this be possible? Is the sun light an example of that? Would the interference occur if the rays were not in phase?

[]'s

João

Cthugha
If the rays are not in phase initially, that basically just introduces an overall offset. The constructive interference occurs if two different waves are in phase at some point. If you now have an initial phase difference, the additional phase difference you need to achieve for interference by having the two beams take different paths is now not 2d = n λ anymore, but a bit shorter or longer.

For interference patterns to occur, it is more important that two beams have some fixed phase relationship. They need not be in phase, but the phase difference should not change over time. Light from the sun does not have this property as it is composed of many wavelengths and the phase changes randomly (due to the random nature of the light emission process) on a timescale of the order of femtoseconds.

Khashishi
If we measure the light pattern on a screen, we are viewing the interference at the screen. Any interference that occurs on the way to the screen doesn't matter, since we are not looking at that point. Different light sources don't interact with each other as they travel through space. They just pass through each other.

If you cross the beams of two lasers, the waves will overlap in the crossed region, but two beams will pass out the crossed region as if nothing happened.

If you cross the beams of two lasers, the waves will overlap in the crossed region, but two beams will pass out the crossed region as if nothing happened.
But if we put a screen in the crossed region, we would see interference right?

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For interference patterns to occur, it is more important that two beams have some fixed phase relationship. They need not be in phase, but the phase difference should not change over time.
Thanks Cthugha. The light I've mentioned was not composed by 2 beams only, but infinite beams that have a randomly phase difference (like the common-light we see in our houses, that is reflected many times). Would this cause a interference pattern?

Cthugha
No, if you have infinite beams at random phases, every possible phase difference is realized and therefore also every possible scenario from constructive to destructive interference (and partial interference in between). In summary all of these contributions cancel out and there is no interference at all.

sophiecentaur
Gold Member
The picture suggests the 'Newtons Rings ' phenomenon. This is visible with 'ordinary' light sources (the old slide projectors were very susceptible). It's only the first one or two fringes that were visible, though. The point is that all the "infinite beams" will interfere with themselves over a small range of angles, because there is a small degree of coherence. Obviously, with a laser source, the pattern will be much stronger and appear over a wider area of any image.
Light from all over a room will never give you visible fringes but once you start to collimate the beam (in a projector, for instance or just light from one direction), the effect starts to appear. The first thing you tend to see is coloured fringes as RG and B cancel at different angles.

The picture suggests the 'Newtons Rings ' phenomenon. This is visible with 'ordinary' light sources (the old slide projectors were very susceptible). It's only the first one or two fringes that were visible, though. The point is that all the "infinite beams" will interfere with themselves over a small range of angles, because there is a small degree of coherence. Obviously, with a laser source, the pattern will be much stronger and appear over a wider area of any image.
Light from all over a room will never give you visible fringes but once you start to collimate the beam (in a projector, for instance or just light from one direction), the effect starts to appear. The first thing you tend to see is coloured fringes as RG and B cancel at different angles.
Thanks sophiecentar, but no one has answered my question yet. Would kashishish light cause interference in the crossed region?

sophiecentaur
Gold Member
Thanks sophiecentar, but no one has answered my question yet. Would kashishish light cause interference in the crossed region?
What is that? I googled and got nothing relevant except your post. I am not sure what you mean by "crossed region" either. It would be best if you googled thin film interference and newtons rings for yourself. You will see plenty of diagrams which should help you understand this better. I think you may be making wrong assumptions about which of the light beams you will actually see in your diagram. This could account for your confusion.

I can say that light arriving from all directions that started off as incoherent won't usually produce visible interference patterns. However, if you look at the colours of oil films on puddles, you are seeing an interference effect and light is arriving from all directions (the sky). The interference is very much diluted in this case because of the large amounts of other light. Birds' feathers and butterflies' wings have vivid colours because of interference (not pigments) and, again, the light arrives from all over the place. In the case of so-called interference filters, the films are very thin and the 'fringes' are very wide - consisting of no more than one minimum, which will be a minimum for only one narrow range of wavelengths. The colours you see are 'complementary' colours and not spectral colours (e.g. bright magenta, where yellow has been eliminated)

What is that? I googled and got nothing relevant except your post. I am not sure what you mean by "crossed region" either. It would be best if you googled thin film interference and newtons rings for yourself. You will see plenty of diagrams which should help you understand this better. I think you may be making wrong assumptions about which of the light beams you will actually see in your diagram. This could account for your confusion.

I can say that light arriving from all directions that started off as incoherent won't usually produce visible interference patterns. However, if you look at the colours of oil films on puddles, you are seeing an interference effect and light is arriving from all directions (the sky). The interference is very much diluted in this case because of the large amounts of other light. Birds' feathers and butterflies' wings have vivid colours because of interference (not pigments) and, again, the light arrives from all over the place. In the case of so-called interference filters, the films are very thin and the 'fringes' are very wide - consisting of no more than one minimum, which will be a minimum for only one narrow range of wavelengths. The colours you see are 'complementary' colours and not spectral colours (e.g. bright magenta, where yellow has been eliminated)
Kashishi is the guy up there, sorry

he posted:

If we measure the light pattern on a screen, we are viewing the interference at the screen. Any interference that occurs on the way to the screen doesn't matter, since we are not looking at that point. Different light sources don't interact with each other as they travel through space. They just pass through each other.

If you cross the beams of two lasers, the waves will overlap in the crossed region, but two beams will pass out the crossed region as if nothing happened.
I want to know if you put a screen at the crossed region of the 2 lasers, would you see interference?

Khashishi
yeah, you will see interference in the crossed region.

sophiecentaur
Gold Member
Two different lasers could not interfere because they would not be in phase (coherent). They would measure (near enough) as the same wavelength, perhaps, but that wouldn't be close enough for an interference pattern to be formed. There is a phenomenon called beating when two radio frequency waves of nearly the same frequency are received and this is caused by the phases of the two, drifting steadily in time and producing alternate high and low amplitude resultants. The interference pattern from the two sources is constantly on the move - sweeping across the area- but not forming an identifiable stationary fringe pattern. The same would be happening with two lasers but I don't know of any method of actually plotting the pattern - you certainly wouldn't see it.

Note: you only get interference when you actually measure the vector sum of the waves that are arriving at a location. (For instance, you 'see' the result of the light being scattered from the screen) With nothing in its path, light does not interfere with itself - the waves are totally independent and do not interact. This makes total sense because you can see an object clearly when the Sun is to one side of you. The sunlight is passing across, in front of you, yet you do not see it (except when there is dust or water droplets in the air in front of you and the light gets scattered).

sophiecentaur
Gold Member
yeah, you will see interference in the crossed region.
Hate to disagree with you but the phase coherence between the two wouldn't be good enough for a pattern. (See above post)

yeah, you will see interference in the crossed region.
I'm afraid it's not that simple, at least experiments proving it are far more complex than just putting a screen at intersection. Also, Paul Dirac claimed the interference of two independent light beams can never occur. In any case here is something interesting about it:

http://prola.aps.org/abstract/PR/v159/i5/p1084_1
- "Interference effects produced by the superposition of the light beams from two independent single-mode lasers have been investigated experimentally. It is found that interference takes place even under conditions in which the light intensities are so low that, with high probability, one photon is absorbed before the next one is emitted by one or the other source."

So if photons are not even "colliding" and if there is no slit where they split and interact with themselves, then what are they interacting with? It sounds as if shining one beam now for a few seconds and then the other 10 minutes later that the pattern would again be there, and not only when you shine the second beam, but also just with the first beam by itself. Unless of course you decided to cheat and not shine the second beam, because then the first beam would know, in advance, and it would not produce the pattern. I'm just kidding, but in reality it's just about as crazy as that, isn't it?

sophiecentaur
Gold Member
I'm afraid it's not that simple, at least experiments proving it are far more complex than just putting a screen at intersection. Also, Paul Dirac claimed the interference of two independent light beams can never occur. In any case here is something interesting about it:

http://prola.aps.org/abstract/PR/v159/i5/p1084_1
- "Interference effects produced by the superposition of the light beams from two independent single-mode lasers have been investigated experimentally. It is found that interference takes place even under conditions in which the light intensities are so low that, with high probability, one photon is absorbed before the next one is emitted by one or the other source."

So if photons are not even "colliding" and if there is no slit where they split and interact with themselves, then what are they interacting with? It sounds as if shining one beam now for a few seconds and then the other 10 minutes later that the pattern would again be there, and not only when you shine the second beam, but also just with the first beam by itself. Unless of course you decided to cheat and not shine the second beam, because then the first beam would know, in advance, and it would not produce the pattern. I'm just kidding, but in reality it's just about as crazy as that, isn't it?
It's strange that people always seem to approach this in terms of light. Things can become much easier when you think about the effects at RF. It's identical but you can just treat it classically. The quantum approach is just one way of looking at it but, as in your post, you find yourself talking about photons "colliding" and I see you actually needed to put that in quotes (haha). Laser people have so much more trouble dealing with this sort of thing because of the practicalities of actually producing what a radio engineer would just refer to as "cw". Your notion of shining a laser for a while then turning it off would actually be introducing Modulation, which would be affecting the bandwidth (in RF terms).
You refer to experiments with independent single mode lasers. How were the frequencies maintained accurately enough? I would assume that they were phase locked in some way (like RF sources, synthesised from a common frequency standard) so they wouldn't be totally independent. Of course, there is absolutely no chance of doing experiments with RF sources of such low power that individual photons can be considered because that would be way down in the measuring noise.

It's strange that people always seem to approach this in terms of light. Things can become much easier when you think about the effects at RF. It's identical but you can just treat it classically.
I haven't heard of double-slit experiment performed with radio or any other em waves besides visible light. I guess receiver antenna could be connected to TV and with proper setup the display would show stripes corresponding to interference pattern. Are there any experiments like that?

The quantum approach is just one way of looking at it but, as in your post, you find yourself talking about photons "colliding" and I see you actually needed to put that in quotes (haha).
It's because collision usually implies the trajectories of colliding entities are different before and after collision, which it didn't seem would be the case with photons interference, but when thinking about it a bit more it seems it actually is. In either case it doesn't make any sense since in that experiment photons don't even come close to each other. It's as if they leave some kind of trails behind, like a boat wake.

Laser people have so much more trouble dealing with this sort of thing because of the practicalities of actually producing what a radio engineer would just refer to as "cw". Your notion of shining a laser for a while then turning it off would actually be introducing Modulation, which would be affecting the bandwidth (in RF terms).
I thought we have technical ability to produce lasers that would emit pretty much identical photons, each one of them. Why is that easier to achieve with radio waves?

You refer to experiments with independent single mode lasers. How were the frequencies maintained accurately enough? I would assume that they were phase locked in some way (like RF sources, synthesised from a common frequency standard) so they wouldn't be totally independent.
http://www.conspiracyoflight.com/LaserInterference/LaserInterference.html

Cthugha
Also, Paul Dirac claimed the interference of two independent light beams can never occur.
My favorite comment on that comes from Nobel prize winner Roy Glauber (from "Quantum Optics and Heavy Ion Physics", Nuclear Physics A Volume 774, 7 August 2006, Pages 3–13):

"When you read the first chapter of Dirac's famous textbook in quantum mechanics [8],
however, you are confronted with a very clear statement that rings in everyone's memory.
Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,
Every photon then interferes only with itself. Interference between two different
photons never occurs. Now that simple statement, which has been treated as scripture, is absolute nonsense."

If you take two arbitrary light beams and filter them, so that their properties (spectral width, spatial shape, temporal shape) become comparable, you will also manage to see interference, if the spectral width is narrow enough. A cool demonstration has been given in "Interference of dissimilar photon sources" by Bennett et al., Nature Physics 5, 715 - 717 (2009), where a tunable laser and spontaneous emission from a quantum dot diode were made to interfere.

sophiecentaur
Gold Member
My favorite comment on that comes from Nobel prize winner Roy Glauber (from "Quantum Optics and Heavy Ion Physics", Nuclear Physics A Volume 774, 7 August 2006, Pages 3–13):

"When you read the first chapter of Dirac's famous textbook in quantum mechanics [8],
however, you are confronted with a very clear statement that rings in everyone's memory.
Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,
Every photon then interferes only with itself. Interference between two different
photons never occurs. Now that simple statement, which has been treated as scripture, is absolute nonsense."

If you take two arbitrary light beams and filter them, so that their properties (spectral width, spatial shape, temporal shape) become comparable, you will also manage to see interference, if the spectral width is narrow enough. A cool demonstration has been given in "Interference of dissimilar photon sources" by Bennett et al., Nature Physics 5, 715 - 717 (2009), where a tunable laser and spontaneous emission from a quantum dot diode were made to interfere.
This is a truly great post and it really justifies the opinion I have held for years. It really brings home the fact that photons really are NOTHING like the little bullets that people want them to be. If photons can only 'interfere with themselves' (and I don't have a problem with that as an idea) it merely indicates that the photon model that everyone starts off with in their heads is total rubbish. Dirac didn't have to be wrong if you think of just what a photon is (could be???).
To address MarkoniF's post which asks if the two slits experiment has ever been carried out with anything but light, it happens every day in a multitude of directional radio and TV transmitting arrays. They are often more complex than just two sources but the nulls and maxima that are produced by your local TV transmitting antenna are absolutely the same as the equivalent optical nulls and maxima.
Dirac says a photon can only interfere with itself. Now this implies that the signals fed to each of a pair of dipoles must contain 'the same' photons. This must even apply when each antenna element is fed via a different amplifier (which does happen!). So the photons - which interfere with themselves are handled by each of the two amplifiers in the system and the probability function that determines the shape of the radiation pattern assumes the same things about the transmitters as it does about the 'slits' in the optical experiment. Well, how about that and what it implies about the nonsense of a little bullet that can go through either or both transmitting amplifiers? These transmitters, in principle, could even have separate oscillators for their drives and merely be phase locked by some drive control mechanism. There is nothing to say that the quantum of energy that is represented by the term 'photon' could not be handled by each transmitter. It's just that the photon cannot be a particle as most of the world sees it.
If that isn't 'the death of the little bullet' then I don't know what is. And such an argument would never have arrived so easily via the path of lasers.
I know this is not particularly revolutionary as there are plenty of people who have a more enlightened view of photons but it is a pretty damned good nail in the coffin which could be appreciated by any receptive mind.

It really brings home the fact that photons really are NOTHING like the little bullets that people want them to be.
How about little bullets that wave a little bit, snake-like, and can split in two and interfere with itself? Kind of like some of these electrons here:

http://www.brown.edu/Research/electronbubble/videos/firstmovie.html

http://www.brown.edu/Research/electronbubble/videos/firstmovieimages/quantizedvortex.png

As far as I know, we can make very narrow beams of light, and it appears the thickness does not variate, so they must have some defined 'cross section' radius, or width and height, which is defined by the peaks of photon amplitude, right? And they also have defined some length since we can emit individual photons with a gap between them, right? So something that has certain cross section radius kind of does look like a bullet, or an arrow, depending on how long they are. Do you know how long photons are?