# What restricts two separte sources of light to act coherent?

#### ovais

Hi all

To observe interference of light waves in Young's Double Slit Experiment one needs to have coherent sources.Some,doubts are coming in my mind regarding coherent sources.
Q1. Will it make sense to talk about a single source as coherent source(not sources)
Also two(or more) sources are said to be coherent if they have same frequency and a constant phase difference.
Q2. Can we call the two sources as coherent if the frequency of both sources keep on changing such that at any time the two sources have the same frequency so that their phase relationship do not affects?
In my text they say if we use two sodium lamps for interference no interference fringes will be observed because the light wave from an ordinary source like a sodium lamp undergoes abrupt phase changes in time of the order of 10^-10 seconds.
Q3. Is it mean that two separate sources couldn't act as coherent because of each source produce wave(light) discontinuously and that at the point of emission their phase varies with time; that is each of the sources undergo *ABRUPT* phase changes with time? Or(and) do the two separate sources don't make up coherent set because(as the correct or another reason) that their frequencies do not match?

Q4. I mean the what I must assume, what is the core problem of creating coherent condition from two independent separate sources?

Q5. Lastly Young made use of sodium light it is said that he produces coherent sources by dividing the the same wavefront through double slit, in his case would the frequencies(both of which are same) were fixed with time(in case of sodium light he used) or it was just their phase differences were remain constant? If the frequency do no change it means sodium light is able,to produce monochromatic light if frequency(and hence wavelength) was changing(keeping phase relationship of two slit as source same) then how did he observe the position of maxima or minima(dark and bright) pattern of interference).

Thanks a bunch
Regards

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1)single source can be used to act as a coherent source by passing it through two slits or through a thin prism(fresnel's biprism).
2)Coherent sources: Two sources are said to be coherent if they produce waves of the same frequency with constant phase difference.

** important part **

3)you have a doubt if 2 separate sources of light eg. 2 bulbs can act as coherent sources. No
reason : Light does not have bulk property of matter. It is a property of each individual atom. As individual atoms emit energy randomly, two independent sources cannot act as coherent sources.
(that solves the major part)

#### ovais

The difficulty I am facing regarding coherent source(s) is mentioned above clearly, I think one needs to answer based on the very questions I mention. Further your last paragraph put me in another question. Light is the property of individual atom, so how can even a single source at an instant produces waves that all have same phase, since we are having wave in all directions and at any time multiple number of atoms may be contributing for waves(light) and vibration of each atom(/electron) is random so an any instant there wil be waves with different phases even for a single source, since even a single source is made up of huge number of atoms.

#### Drakkith

Staff Emeritus
2018 Award
There are no perfectly coherent sources. All sources will emit a range of wavelengths which will be coherent to some degree or another.

#### f95toli

Gold Member
There are multiple answers to this question depending on how deep you want to go into quantum optics.

First of all, yes coherence is a property of a single source. A laser produces coherent light, whereas e.g. a incandescent light bulb emits thermal light.
Now, coherence is in real life always a matter of "degree", there are -as Drakkith has already pointed out- no perfectly coherent sources; some lasers are better than others in terms of temporal (in time) and spatial coherence.

Also, it is worth pointing out that if you want to do this "properly" (quantum optics) you need to keep track of the state of the light; it turns out that a Coherent state (laser)is very different from .thermal state (black body radiation), it is also very different from a single photon state (also known as a Fock state) in that it does not have a specific number of photons associated with it. Hence, you can't think of coherent light as a stream of photons.

#### ovais

Ok I understand that there can be no perfectly coherent sources rather there is something we can speak of is degree of coherence their can never be a perfect coherence as notified by Drakkith. This is one aspects taking of the incapacity of sources to produce a unique or sharp wavelenth and hence reducing scope for a perfect coherence. Now I want your attention to an statement given in my text where it says that the source(sodium light) undergoes abrupt *phase* changes and concludes that light from two indipendent sources will not have any fixed phase relationship and would be incoherent(see sentence just above Q3 from text). So here the reason for incapacity of two independent sources to act as cohereny sources is due to phase problem(that phase changes abruptly) it is not talking about the problem of getting unique wavelength(it appears that for the sake of simplicity they assume that source is producing a sarp wavelenth, may be I am wrong guide me on this) but according to them the thing is that the phases of wave keeps on changing. And to get a fixed phase relationship Young used an ingenious technique to 'lock' the phases of waves by emanting light of single source from two slits S1 and S2 so that any phase change in the main source will manifest in S1 and S2. My question so what is restricting the two independent sources two act coherent- 1: their incapacity to produce unique sharp wavelengt or their incapacity to produce wave with abrupt phase changes resultimg in varying phase relationship(see Q3)

#### f95toli

Gold Member
I think you are asking if the problem is frequency or phase instabilities (it is in this context easier to think about frequency than wavelength).
The answer is that the two are -generally- just two different ways of describing the same instability (you can "convert" frequency noise into phase noise, the two are generally proportional); if the frequency fluctuates you will also get phase noise and vice versa.

#### ovais

I think you are asking if the problem is frequency or phase instabilities (it is in this context easier to think about frequency than wavelength).
Exactly:) this is what I want to know clearly.
The answer is that the two are -generally- just two different ways of describing the same instability (you can "convert" frequency noise into phase noise, the two are generally proportional); if the frequency fluctuates you will also get phase noise and vice versa.
Their can be no doubts that a fluction in frequency will being about a change in phase such that there by incapcity of souce to give monocromatic light there will come temporal(time varing) phase relation which is highly random. However as indicated in text the other cause of incapacity is the inabilty of source to generate conituoues wave with varing phase(even for a particular frequency) I want the response of people here upon my understanding that phase unstabilty can occur even if source(magically) is producing monocromatic light. I mean the problem of inconsistancy of phase(or probelm of coherence) will occur even when their is no fluctuating frequency from source, this doesn't mean I am rejecting the fact that a change in frequency will being change in phase.

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#### ovais

Just a little correction of my earlier post(which has already taken into account:) by people here) so that other people who see it remains clear what is being said. Here what is to corrected in words
question so what is restricting the two independent sources two act coherent- 1: their incapacity to produce unique sharp wavelengt or their incapacity to produce wave with abrupt phase changes resultimg in varying phase relationship(see Q3)
...or their incapacity to,produce wave with stable phase. That is the problem that their comes abrupt phase variation.

#### f95toli

Gold Member
phase unstabilty can occur even if source(magically) is producing monocromatic light. I mean the problem of inconsistancy of phase(or probelm of coherence) will occur even when their is no fluctuating frequency from source, this doesn't mean I am rejecting the fact that a change in frequency will being change in phase.
If the phase is varying randomly your source will not be coherent and you will not see interference. The problem is that I can't think of a real source where phase and frequency can vary independently, they are connected in any source that uses an oscillator or a cavity (e.g a laser) so the question is a bit hypothetical.

Also, note that it IS possible to produce interference between photons coming from two different sources, it is just very difficult. This was demonstrated experimentally a few years ago.

#### ovais

If the phase is varying randomly your source will not be coherent and you will not see interference.
Totally agree I have no doubts in this.

The problem is that I can't think of a real source where phase and frequency can vary independently.
I don't understand why you believe this.

A source produces waves(light radiation(s)) which has phases. The phases of waves has different values in space, further at the points (or may be even at the particular point of emmision with the pasaage of time) of emmison of waves(near or closed to source) the phase of wave will generally be different keeping in Mind that emmision of light is due to vibrations or movements electrons which is completely random( I don't know I am explainng it right So at any point the phase at the emerging point can change abruptly indipendeny of the frequency change or atleast the phases of waves at different points from where the waves are emerging at any point of time will not simply be same

#### f95toli

Gold Member
Yes, but what you are describing is -sort of- essentially a thermal source which will have a broad frequency spectrum. What you asked about was a source which emits at a single frequency but had a random phase, and I can't think of a source that behaves that way; it certainly excludes any source based on an oscillator or a resonator (where phase noise is also turned into frequency noise).

In e.g. a laser you have that the instantaneous frequency is given by

$$\frac{1}{2\pi} \frac{d \phi}{dt}$$

Hence, any variation in phase will also result in a change of frequency; and it follows that the phase for a truly monochromatic source have to evolve linearly (i.e. a constant phase shift).

#### Andy Resnick

<snip> Now I want your attention to an statement given in my text where it says that the source(sodium light) undergoes abrupt *phase* changes and concludes that light from two indipendent sources will not have any fixed phase relationship and would be incoherent(see sentence just above Q3 from text). So here the reason for incapacity of two independent sources to act as cohereny sources is due to phase problem(that phase changes abruptly) it is not talking about the problem of getting unique wavelength(it appears that for the sake of simplicity they assume that source is producing a sarp wavelenth, may be I am wrong guide me on this) but according to them the thing is that the phases of wave keeps on changing. And to get a fixed phase relationship Young used an ingenious technique to 'lock' the phases of waves by emanting light of single source from two slits S1 and S2 so that any phase change in the main source will manifest in S1 and S2. My question so what is restricting the two independent sources two act coherent- 1: their incapacity to produce unique sharp wavelengt or their incapacity to produce wave with abrupt phase changes resultimg in varying phase relationship(see Q3)
Part of the confusion here is that there has not yet been a clear distinction between *temporal* coherence (due to the frequency bandwidth) and *spatial* coherence, which is a measure of how large the source is. Certainly, a source can be temporally coherent and spatially incoherent- spectrally filter sunlight- and light can also be spatially coherent and temporally incoherent- spatially filter sunlight. Lasers typically have a high temporal and low/moderate spatial coherence: speckle results from spatial coherence, so using a laser for any wide-field optical system (like a Mach-Zender interferometer), one should spatially filter the light prior to the system.

Young's double slit demonstration uses spatial, not temporal, coherence to create interference fringes and can be used to, for example, measure the diameter of stars. This principle was extended to intensity interferometry (generally called the Hanbury Brown and Twiss effect).

An excellent introduction to optical coherence is Wolf's "Introduction to the theory of coherence and polarized light".

#### ovais

The few above posts make me think that I have some misconception regarding, with what phase a wave emerge from its source" leaving the temporal and spatial incoherence now for now. Let me put what I consider. I want to tell what I consider for light sources in two parts. First for a discussion of single,point of the source. In second I will talk about my intitution for different points on a sourec.

FOR SINGLE POINT ON A SOURCE

I consider that the source emit light from so many points from its illuminating surface. And if I focus on the phase of emerging wave just only at a single point on the source itself(that is at the same pointfrom where waves are comming) then due to randomness of electron movements in the source, ***the phase at which the wave is emerging from the source keep on changing abruptly*** (Not only that phase of waves reaching some point ahead changes due spatial incoherence).

Is my this thinking right or wrong?

FOR DIFFERENT POINTS ON THE SOURCE

I consider that as the source is producing light. There are several points from where waves are being emerging. I consider at any instant the phases at the different points(all of which lies itself on the illuminating surface of source) have different phases reason being same that light is produces by motion of electrons which move in comple,random way.
Is my this thinking corrct or not.

Thanks a bunch for all of you for continous support :)

#### Andy Resnick

<snip>I And if I focus on the phase of emerging wave just only at a single point on the source itself(that is at the same pointfrom where waves are comming) then due to randomness of electron movements in the source, ***the phase at which the wave is emerging from the source keep on changing abruptly***
For a broadband source, yes; for a monochromatic source, no.

F<snip>There are several points from where waves are being emerging. I consider at any instant the phases at the different points(all of which lies itself on the illuminating surface of source) have different phases reason being same that light is produces by motion of electrons which move in comple,random way.
Not sure what you are asking here.

#### ovais

For a broadband source, yes; for a monochromatic source, no.
The answer is yes, definitely as being pointed out by you in earlier posts I really like it :). I however doubts that the answer turned 'No' for monocromatic light. See what I am observing and wanting your response over it is that, the emmision of waves due to movement/vibration/jumping of electron. Each time is move or jump(whatever the way use to be) it emits light wave which must have some phase. I consider that as(even in our imaginative,monocromatic source) the movement of electron is random and hence if (from a given point at source) at time t the wave(of frequency n) comes (at the comes of emergence just from where it is emmerging) with some phase then after little time t' the wave from the same point(source being monocromatic light will come with same frequency) but will have phase at the emerging point not same as that of the wave that came at time t.

Is this mentally right or wrong. You however has already said no but I doubt weather you understood what I was saying or not. And I need not just yes or no I also
need a brief explanation clearing the basics of any relation(if exists) between randomness electron jump/movement and phases of the emerging wave. I mean what defines phase of the emerging wave(at the point on the source from where wave is emmerging) for the case of monocromatic source in particular and broadband sources in general.
Not sure what you are asking here.[/

Not sure what you are asking here.
Here I am talking about same thing but this time I am focusing say two different points A and B of the source(monocromatic source) at a given instant if time say t.
So here i am interested to observe two differenet(as opposed to a single point i selected in previous observation and observe that point's wave phase with time) points simultaneously and i want to observe the phase of waves emmerging (phase at the points on the source which is monocromatic from where waves are emmerging) from thse two points A and B at a time say t. My thinking is that the phases of the waves at points A and B will again be not same(even though frequency of light at A and at B is same). Reason i can is since electron jumping is random(though fixed in the way that produce only definite energy or frequency in our case of monocromatic light) but randomness or time gap of jumping will result in different phase.

please guide me on these things, if these are my misconceptions or can you explain to me the real pictute?

#### Drakkith

Staff Emeritus
2018 Award
I consider that as(even in our imaginative,monocromatic source) the movement of electron is random and hence if (from a given point at source) at time t the wave(of frequency n) comes (at the comes of emergence just from where it is emmerging) with some phase then after little time t' the wave from the same point(source being monocromatic light will come with same frequency) but will have phase at the emerging point not same as that of the wave that came at time t.
You can't have monochromatic light from a source that varies randomly. This random motion of the electron would result in different frequencies emitted at different times and you end up with a broadband source. In any case, the emission of light from an object is much more complicated than just "movements of electrons". Entire molecules and atoms can move in different ways and emit light.

#### Andy Resnick

<snip> And I need not just yes or no I also
need a brief explanation clearing the basics of any relation(if exists) between randomness electron jump/movement and phases of the emerging wave. snip>

please guide me on these things, if these are my misconceptions or can you explain to me the real pictute?
I think you need to do some more background reading first.

#### ovais

Ok I will have a background reading for the above. Will you suggest any book on this which talks about this within my level?

From what said in the few above post I came to know a fact(though I am looking for an explanation for which I ask for a suggested reading) that a change of phase of light(at the point of emmergence) can only be due to change in frequency.

But will love to know as final review the direct straight answers of my questions in the very first post(Ist question is cleared ithink already). It would be a favour if you give some of your precious time to give a direct answer to them especially 2nd and 5th question.

#### ovais

I am writing this just for the purpose to get my this thread a meaning in the hope of getting some more help. I am really sorry for my weak mind which still not understood the after so much help :-(

#### Drakkith

Staff Emeritus
2018 Award
I am writing this just for the purpose to get my this thread a meaning in the hope of getting some more help. I am really sorry for my weak mind which still not understood the after so much help :-(
I think part of the problem, at least for me, is that I'm having trouble understanding what you're asking. You are making frequent grammar errors that make it very difficult to understand what you're asking. For example:

Q2. Can we call the two sources as coherent if the frequency of both sources keep on changing such that at any time the two sources have the same frequency so that their phase relationship do not affects?
The last part, "so that their phase relationship do not affects" make no sense at all. I literally don't know what you're asking here. If I were a little more knowledgeable in this area I might be able to work it out, but right now I don't know what you're asking. There's plenty of other example like like this one too.

I don't mean to offend you, but if we can't understand you, we have little chance of helping you. I have a language disorder myself, and I can tell you that I spend a great deal of time making sure that what I've written is worded as clearly and simply as I can make it.

#### ovais

What I was saying is that suppose I have two separate sources of light. The sources are unable to give a constant frequency. For a simplest theoretical discussion let the frequency of one of my source is given by f= k + sin(bt) and let the other source also produces light of frequency given by f= k + sin(bt) where k & b are constants and t is any time after one of the source is illuminated, clearly the will also be same for both the sources. So here the frequency of the sources is not remaining constant. The frequency of the both the sources keep on changing but at any time their frequency will come out to be same. This will mean if the cycle of first wave speeded up the cycle of second will also be speeded up so that phasor difference between them will still remain the same. Imagine two particles at two different points(making some angle with the center of circle),moving on the same circle with same angular frequency. Under such condition their phase difference will remain same. Now of one the particle changes its angular frequency(started moving faster on the circle) their the angle(phase difference) between them will be changed. However if both the particles speeded up their angular frequency by same amount then I think the angle they had between them( their initial phase difference) will remain as such. This is how I am relating the phase difference of two waves with (angular) frequency. In the above example I noticed that two particles can have a constant phase difference even if their frequency keep on changing. So my that question was about the possibility that if I have two sources that emit waves whose (individual) frequency keep on changing in such a way the two frequencies at any time possessed the same value(though both are changing) that their phase difference should remain same and they should be called coherent sources.

#### Drakkith

Staff Emeritus
2018 Award
Yes, if the two sources change in such a way so that the phase difference between them is always the same, then they are coherent.

#### sophiecentaur

Gold Member
You seem to be proposing two sources that are not only synchronous and monochromatic but with modulations that are also synchronous. If you were talking in terms of two RF sources, you would be in with a very good chance that the two sources could be set up and keep synchronism, independently of one another for an extended time (years, possibly). such that they could produce a stable interference pattern The idea of having two independent light sources on the same terms seems very unfeasible. The nearest you could get might be two lasers, slaved to a third, reference source. The modulation might not be such a problem to synchronise.

As we're in the fringes of practicability, could you give an idea of what the application of this could be? Perhaps there would be an easier way of achieving what you want to do.

#### ovais

Yes, if the two sources change in such a way so that the phase difference between them is always the same, then they are coherent.
Thank You I now got the answers to my first and second questions. To effectively get the answer to my 3rd and 4th question i should ask one straight question that can lead to the answers of 3rd and 4th question. Actually I will ask two questions.
The straight question is," Let P be one of the point on the source(producing magically only monocromatic light) from where waves are emerging, Let i represent my wave (light) function as a function of distance x from the point of emission (on source) and time time t(t being zero at the time of emission. Do the phase of wave at x=0 bears a constant value for all values of t?"
Let Q be another point on the same source(monocromatic) , the phase of wave from point Q at t=0, have same value as the value of phase of wave from P at t=0?"

You seem to be proposing two sources that are not only synchronous and monochromatic but with modulations that are also synchronous.
sophiecentaur these may be the things i require but i unable to understand these terms as related with light and waves. I mean synchronous, modulations etc what are these and what makes sources syncronous and unsyncronous and where does they come into play at the first place?

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