Can interference occur without the use of single slit?

[Ahsan Khan]

I wonder can a sustained interference pattern be obtained in Young double slit experiment if we do not use single slit between source of light and the double slits when one has a monochromatic source in the experiment.

Regards

 

[Nugatory]

You need a source of coherent light. The single slit is by far the cheapest, easiest, and lowest-tech coherent light source, but any coherent light source will do.

 

[Ahsan Khan]

You need a source of coherent light. The single slit is by far the cheapest, easiest, and lowest-tech coherent light source, but any coherent light source will do.

First of all thank you for giving your precious time for the reply.
Say the only information provided to me is that my source is monochromatic, the questioner was asking me if you do have a monochromatic source and two slits after it, will you get any sustained interference pattern on the screen placed after some distance.

 

[Ahsan Khan]

It appears as he was asking that Could a pure monochromatic source amount to a coherent source?

 

[my2cts]

Interference always occurs but to make it visible you need a coherent source.
If the source the result is a superposition of interference patterns in which the intensity variation is erased.

 

[Ahsan Khan]

Interference always occurs but to make it visible you need a coherent source.
If the source the result is a superposition of interference patterns in which the intensity variation is erased.

Can a(single) pure monochromatic source(without single slit) act as coherent source?

 

[my2cts]

Such a source lacks spatial coherence and can be seen as a superposition of spatially coherent sources (think of your source as consisting of adjacent slits). You will observe the interference patterns of each of these slits superimposed on each other. This will erase the characteristics of the individual interference patterns

 

[phinds]

It appears as he was asking that Could a pure monochromatic source amount to a coherent source?

Well I guess it COULD, but there is no reason to assume that it does in any particular case. Coherent is more restrictive than monochromatic. Do you understand the definitions of the terms?

 

[blue_leaf77]

Monochromaticity ensures perfect temporal coherence, but not always with spatial coherence. For example you have a light bulb (extended source) containing one species of atom, and further assume these atoms magically emits one exact frequency from $t = -\infty$ (perfect temporal coherence). These atoms do not,in general, emit radiation all in phase, hence the spatial coherence is limited. In this case you still need a pinhole.

 

[my2cts]

For interference you need both temporal (monochromaticity) and spatial (collimation) coherence.
If you use an imaging system you can do without temporal coherence.

 

[blue_leaf77]

So whether one can maintain the interference pattern depends on the type of the source. If this source is of one single atom, then yes one doesn't need the first pin hole at all.

 

[Ahsan Khan]

Such a source lacks spatial coherence and can be seen as a superposition of spatially coherent sources (think of your source as consisting of adjacent slits). You will observe the interference patterns of each of these slits superimposed on each other. This will erase the characteristics of the individual interference patterns

OK what about this(image below)? Only two openings(two slits) on a monochromatic source.

 

[Ahsan Khan]

Will sustained interference pattern observe in this source is assumed to be perfectly monochromatic

 

[Ahsan Khan]

Yes phinds I know their definitions the confusion I am having(which is very well being getting clear through you guys lies into understand whether a(single) monochromatic source be turned into a coherent source any how?
Like what I shown in the figure.

 

[Ahsan Khan]

Blue_Leaf77 your. statement, Monocromocity ensures temporal coherence but not always spatial coherence, is very informative. But I will be very thankful to you if tell me it in more simpler way of my level.

As per the assumptions you also took that let us suppose that the extend source somehow(magically) produces only single sharp wavelength, then how do them(atoms), in general will not emit waves all in phase, causing limited spatial coherence.

If you tell this in more descriptive way I will be very thankful to you I am sorry for my very little basic knowledge.

The same think can be answered if you just tell me if their will be sustained interference in the case of which a picture I sent with a little backup of knowledge.

Regards

 

[my2cts]

OK what about this(image below)? Only two openings(two slits) on a monochromatic source.

If you would read my statement you would not ask.

 

[Ahsan Khan]

I read your statement and see it very seriously. But their is some difference I noticed between what I asked at first in my question which you clearly answer in that very reply and the situation(something different with one source please do look picture you will get an idea what different thing now I want to look at) which is in the picture now.

As the problem of not having spatial coherence is appear to be absent in this case of picture. I beg you to reply in that case in more open way for I don't hesitate to beg for knowledge as knowledge is the only thing worth begging.

Regards

 

[blue_leaf77]

Monochromatic light only has one wavelength, only contains one harmonic, in math form you will write monochromatic light as $E_0 \cos{\omega t}$. Such wave when compared to its copy will have fixed phase relation from $-\infty$ all the way up to $+\infty$, that is $\Delta \Phi \neq f(t)$. This means this wave has infinite coherence length which is the definition of perfect temporal coherence. I hope this link can help you further: http://www.rp-photonics.com/coherence.html

 

[my2cts]

Your picture has no information on the spatial coherence of the source.

 

[Drakkith]

Will sustained interference pattern observe in this source is assumed to be perfectly monochromatic

Yes. The light emitted from each slit will interfere and form an interference pattern on the screen.

 

[my2cts]

Yes. The light emitted from each slit will interfere and form an interference pattern on the screen.

I disagree, anything is possible. It completely depends on how each of the openings is illuminated. The picture contains no information on this.
If both openings are illuminated from the same point source an interference pattern will form, namely a coherent sum of the individual slit diffraction patterns. Note that the two slits are then each illuminated from a different direction. If the source is spatially extended the interference pattern is the sum of all such patterns, one per source point. This sum is incoherent if the source points are incoherent. The more extended the source the less of an interference pattern will remain. If all points of the source are coherent, some complex interference pattern will result.

 

[Drakkith]

This sum is incoherent if the source points are incoherent.

How can you get incoherent source points if the source itself is given as a monochromatic source?

 

[my2cts]

A monochromatic source is temporally coherent but not necessarily spatially coherent.
For the latter, light from different directions also has to have a phase relation.
If monochromatic light comes from a diffuse scatterer, such a phase relation is lost.

 

[Ahsan Khan]

Yes. The light emitted from each slit will interfere and form an interference pattern on the screen.

I disagree, anything is possible.

Here are the things hooking up. I fail to get a common answer, people even in my Institute are telling different answers without giving a descriptive answer for their "yes" and "no" and I have my own thoughts on "yes" and "no" for the above question. Which if cleared sufficed the purpose of the thread. And I am here just to clear the doubt and I feel as opposed to philosophy where disagreements at a subject are allowed, physics is an exact science, answers with disagreements needs to consider again.

Regards

 

[Drakkith]

A monochromatic source is temporally coherent but not necessarily spatially coherent.
For the latter, light from different directions also has to have a phase relation.
If monochromatic light comes from a diffuse scatterer, such a phase relation is lost.

And how does this tie into the example given by the OP?

 

[blue_leaf77]

Ok there seems to have been a little debate here, I feel sorry for the thread owner.
Anyway after some deep review of my past lectures, I apologize I must revise my answer. Previously I was arguing that spatial coherence must be taken into account. But it turns out that as long as all emitters are monochromatic of the same wavelength, the coherence area is infinite. So one won't have to place a single slit first. This is so because coherence area is defined as an area within which two points can maintain its phase difference for all times. If all emitters are strictly monochromatic, then when I place two superfast spectrometers at any two points in space, they will always measure one wavelength for all times => the distance between two consecutive wavefronts stays constant for all time, otherwise there will be new frequency. This implies that the phase difference between those 2 points is constant, if one were to place two pinholes at those points the interference behind it will be fixed for all times. As time flows, different phase fronts will traverse those pinholes but the phase difference between them is unchanged. An example of an extended source with all monochromatic emitters might be illustrated in this picture: http://en.wikipedia.org/wiki/Coherence_(physics)#mediaviewer/File:Spatial_coherence_infinite_ex2.png

Irregularities in the source shape, such as that caused by diffuse reflection, only affect the ugliness of phase fronts. The above is true as long as all emitters are frozen in space, if they move there will be Doppler shift due to the movement itself and random collisions which can cause random phase jump.

 

[my2cts]

And how does this tie into the example given by the OP?

It monochromatic light comes from a diffuse scatterer there is no spatial coherence and an intereference pattern is not visible.

 

[Ahsan Khan]

... it turns out that as long as all emitters are monochromatic of the same wavelength, the coherence area is infinite.

OK this statement is really useful(helpful), let me tell you what I understood by this very useful statement: I assume that you are saying as long as the source is (perfectly) monochromatic the phase of waves at every point on the source is the same their will be no phase lagging or phase leading of waves at the points of their emergence.

Also it would eventually negate the possibility of a case that a(particular) point on source is emitting wave but at that same instant of time no wave is emmeted by one of the other points on the source. Because this very thing was also a matter of disagreement between lecturers in my Institute. To exactly clear what I mean I am attaching a picture. So that you can help me better.

Regards for so much help. :-)

 

[Drakkith]

It monochromatic light comes from a diffuse scatterer there is no spatial coherence and an intereference pattern is not visible.

Perhaps, but in the OP's example the light isn't scattering. The source is simply being blocked at all points except at two small slits.

 

[Ahsan Khan]

Perhaps, but in the OP's example the light isn't scattering. The source is simply being blocked at all points except at two small slits.

Rightly said sir. I just need one more thing as asked in my earlier post) to be clear with due reason. Once you say something one that I will reflect over it with based with reasoning(perception) that I, why some of my lectures tell and make me feel that still(the picture's situation) will not result sustained interference, so that I may be a good teacher with less doubts.
:)

 

[blue_leaf77]

it would eventually negate the possibility of a case that a(particular) point on source is emitting wave but at that same instant of time no wave is emmeted by one of the other points on the source.

This statement of yours is out of place. If there is such discontinuous wave train, it means the light source is not monochromatic. Monochromatic waves are those having one frequency epxressed mathematically as either sine or cosine function, hence they must be continuous. It's that and must be that.
Well then you may argue that one can have emitters than can be controlled electrically such as that in your last picture. However monochromaticity defines an extremely strict requirement that this wave must start at $t = -\infty$ and ends at $t = \infty$. In spectral domain monochromatic wave has a delta function spectrum located at its oscillation frequency. You can prove it by Fourier transforming such discontinuous wave, you should find the spectrum is not a delta function.

 

[blue_leaf77]

It monochromatic light comes from a diffuse scatterer there is no spatial coherence and an intereference pattern is not visible.

Let's observe a picture I attach. The incoming wave has both perfect temporal and spatial coherence. As I have said the irregularities in the surface only change the structure of reflected wavefronts, it may look as ugly as it can take but as long as there is no change in the surface structure the reflected wavefronts will stay as they are for all times. If one observes what is happening at two points A and B in space, since the reflected wavefront shape that traverses these points is unchanged in time the phase different between those points will also be kept fixed. And now let's remember that what prevents us from seeing interference pattern is that if it fluctuates very rapidly, this rapid fluctuation of interference pattern must have been caused by rapid change in the state of the source. So what if the source state doesn't undergo any change, the emitted wavefronts won't undergo any change either.

 

[siddharth23]

The two slits act as two sources of light, and being from the same source originally, they are coherent.

If you can get two coherent sources, then yes, interference will occur.

 

[Drakkith]

Rightly said sir. I just need one more thing as asked in my earlier post) to be clear with due reason. Once you say something one that I will reflect over it with based with reasoning(perception) that I, why some of my lectures tell and make me feel that still(the picture's situation) will not result sustained interference, so that I may be a good teacher with less doubts.
:)

I can't understand what you've said here.

 

[sophiecentaur]

Let's observe a picture I attach.

Unfortunately, that picture gives the wrong impression of what actually happens to the incident wave fronts. Each piece of the irregular surface will give rise to a set of wavelets (Look up Huygen's Principle) and all those wavelets will add together to give a pattern which is far less 'detailed' than what you have drawn. It will, in fact, produce a smooth looking shape that is curved - showing that the original plane wave front has been diffused. It helps to bear in mind the basic rules of diffraction - the relevant one here is that small structures (i.e. the irregularities) produce broad diffraction patterns and it is only large structures (like pairs of Young's slits, separated by several wavelengths) produce fine structured interference patterns.

 

[Claude04]

Thanks for these infos !

 

[Ahsan Khan]

This statement of yours is out of place. If there is such discontinuous wave train, it means the light source is not monochromatic.

OK so this means that the correct position is that such a source can't be a monochromatic source as earlier also told by diratkkh.

It would be even higlhy appreciable to remove even this trace of doubt from my mind.

A source(with discontinuous wave trains), as shown in my pic can't be a monochromatic one I understand how it can't be monochromatic. Now my question is that if the source is non-monochromatic does it emit discontinuous wave train(of same wavelength) as shown in my picture which eventually cause it to behave as a non-monochromatic source or does it emit continuous wave of different wavelengths from its(non-monochromatic source).
My question is about what causes a source to act non-monochromaticaly based on wave/atomic level.

Drakkith, Sir this is what written above I wanted to say.

Thanks Regards

 

[Drakkith]

Now my question is that if the source is non-monochromatic does it emit discontinuous wave train(of same wavelength) as shown in my picture which eventually cause it to behave as a non-monochromatic source or does it emit continuous wave of different wavelengths from its(non-monochromatic source).

Both.

My question is about what causes a source to act non-monochromaticaly based on wave/atomic level.

The acceleration of charges is not uniform or continuous, giving you a range of wavelengths.

 

[blue_leaf77]

give a pattern which is far less 'detailed'

It is in far field region where the field is given by the FT of the scatterer, in fact diffraction physics guys call these spherical wavefronts in far field as Ewald sphere. But in near field, I think it should still resemble the shape of its scatterer. Anyway the point I uploaded that picture was to emphasize that in that situation any two points in space will always maintain its phase difference all the time.

My question is about what causes a source to act non-monochromaticaly based on wave/atomic level.

There are many kinds of line broadening mechanism, the most natural one is natural broadening caused by the fact that excited electron has finite lifetime. The others include collision broadening, Doppler broadening, etc.

 

[Ahsan Khan]

Both.

Wow good. Please do also teach me which one of the above limitation is easier to control. I mean if we were to make a close monochromatic source which of the above problem come more as a hurdle or to say what scientists actually do, in coming technology by which they are able to make sources close to monochromatic one like laser(I am not sure is laser a close to monochromatic source)

The acceleration of charges is not uniform or continuous, giving you a range of wavelengths.

When you say acceleration of charges is not uniform what it actually referring to?

Does it mean the various charges in the bulk of the source do not have same acceleration at any point of time causing different wavelengths(at a single point of time) or does it mean that any time all charges have same uniform acceleration but that acceleration of different charges can keep same value with the passage of time.

May be you will say, O May God how many questions do he ask? :) I am so sorry for that but I hope you will answer them. Lol

 

[Ahsan Khan]

There are many kinds of line broadening mechanism, the most natural one is natural broadening caused by the fact that excited electron has finite lifetime. The others include collision broadening, Doppler broadening, etc.

Sir you have explained a lot of good things I really appreciate it. But I do not understand the above terms like broadening mechanism, role of finite life time of excited electrons etc. It would be very helpful further if they may be explained simply so that I can have a clear idea.

Regards

 

[blue_leaf77]

line broadening = broadening of spectrum from delta function (monochromatic) to something else w/ nonzero width (polychromatic). Google can help you a lot further.

 

[brianhurren]

You need a source of coherent light. The single slit is by far the cheapest, easiest, and lowest-tech coherent light source, but any coherent light source will do.

It is a coherency filter, much like a pin hole.

 

[Drakkith]

Wow good. Please do also teach me which one of the above limitation is easier to control. I mean if we were to make a close monochromatic source which of the above problem come more as a hurdle or to say what scientists actually do, in coming technology by which they are able to make sources close to monochromatic one like laser(I am not sure is laser a close to monochromatic source)

A laser is not a monochromatic source. It has a very narrow bandwidth, but still has a bandwidth. Bandwidth means it emits a range of wavelengths. For example, a laser may emit light within a range of 499-500 nm. Or perhaps 499.9 - 500.1 nm.

It's not about which one is 'easier' to control. The fact is that a real source is both discontinuous (since you have to turn it off and on) and emits a range of wavelengths. We cannot get rid of either one, so we can't make a perfectly monochromatic source.

When you say acceleration of charges is not uniform what it actually referring to?

Does it mean the various charges in the bulk of the source do not have same acceleration at any point of time causing different wavelengths(at a single point of time) or does it mean that any time all charges have same uniform acceleration but that acceleration of different charges can keep same value with the passage of time.

The former I think. I'm not quite sure what you're trying to say with the second half of that sentence. In a bulk material you will have charges moving at difference velocities, in difference directions, and undergoing different acceleration at any point in time. The acceleration isn't constant or continuous for any individual charge either. It's a real mess down there.

 

[Ahsan Khan]

It's not about which one is 'easier' to control. The fact is that a real source is both discontinuous (since you have to turn it off and on) and emits a range of wavelengths. We cannot get rid of either one, so we can't make a perfectly monochromatic source.

Thank you Drakkith. OK we can't get rid of anyone. I still need to know what actually Young did by placing the single slit between source and double slits. I mean by using it did he corrected the discontinuity of wave trains which is also a cause of phase change(and not letting coherence) or it corrected the changing frequency problem of the sodium source or both. I again want to take you back at the statement of textbook where it says that their is "abrupt" phase changes in the phase if waves and that Young uses an indigenous techniques of "locking" the phase. I want to know (1).if the text talking about "abrupt" phase change due to discontinuity of wave fronts or due to fluctuating wavelengths or both,(2) when they say Young " locked" the phases by using single slit do they mean by doing this discontinuity in wave trains get eliminated or do they mean by doing this problem if fluctuating phase is removed or both.

I am attaching the pages of the textbook in the next post.

The former I think. I'm not quite sure what you're trying to say with the second half of that sentence. In a bulk material you will have charges moving at difference velocities, in difference directions, and undergoing different acceleration at any point in time. The acceleration isn't constant or continuous for any individual charge either. It's a real mess down there.

Thank you. I am sorry that the second portion of my that post was written with a mistake and that's why you couldn't get it. I apologise for this. I must make that only change which was written wrong rest you can go back to it to see it.

The mistake was in last sentence its can't keep(instead of can keep) the same value of wavelengths with passage of time.

Regards

 

[Ahsan Khan]

Pictures

 

[Ahsan Khan]

Typed, just to get into discussion the forgotten post. It would be very helpful if my last two posts be responded as the earlier ones were done. It's really feel very good that people here in our PF are very helpful.