Can interference occur without the use of single slit?

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

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.

 

[ovais]

... 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.

 

[ovais]

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.