Dear Marc,

Your question is very fundamental and leads to an important quantum mechanics concept, the complementarity. In this special case is visibility and which slit concept which play role, and are corresponding to the wave and the particle nature of the light.

The near field gives enough knowledge about the particle feature - which slits the light passes - Let's call it D.

The far field gives information about the wave nature [momentum of light] - if whether they are in phase or out of phase. Let's call this value V.

The sum of "which slit information" and the "visibility" is bounded to unity. The near and far field are both two extreme cases, where for the first case V=0 and D=1 and in the second case V=1 and D=0. Therefore, any intermediate case gives a partial information about "which slit" and the "visibility". Thus, as you know well, the fringes visibility decreases by moving detector plane toward the slits.

Hope that this clarifies some points. By the way, the inequality for visibility and which information is V^2+D^2

May be this link will help you...

http://www.youtube.com/watch?v=DfPeprQ7oGc

Dear Mohit,

Thank you for the link.

What is described in the video is well-known but unfortunately doesn't answer my question: what does happen when the screen is very close to the slits? Are there interferences on the screen still?

Before you pose a question, search researchgate: a similar question and answer already exists!

Vang Le

Aalborg University Hospital

"Quantum double slit experiment."

I watched this video two years ago: http://www.youtube.com/watch?v=DfPeprQ7oGc

Dear Marc,

Well in that case please take a look on http://www.studyphysics.ca/newnotes/20/unit04_light/chp1719_light/lesson58.htm

Please consider example-1, where you can play with L= length from the screen with slits to the viewing screen (m)... put your desired value... but if you are considering L=0 or minimum values than you can calculate, the Lemda (λ) or the wavelength of the light source that you have used which will give you same light color in interference pattern observed on screen, is also going to zero or minimum value.

This is what I understand. But you can explore more by just studying the examples given on the link. Hope it will address your question .

Dear Harry,

I don't understand why you send me again the same link to the video.

The question "Quantum double slit experiment" from Vang Le was about his critics of this video: "the video is too simple and naive/misleading. I can forgive the simpleness because it aims for broad audience, but I don't believe its claims etc.".

My questions are very specific as they are specifically about the distance D from the slits to the screen.

In the very long discussion (122 answers!) which followed Vang Le's question I don't see that the problem of the distance D I focus on was considered, do you?

Of course if you know the answers I would be grateful if you could give them to us.

Dear Mohit,

Thank you for the link.

However, what I am looking for are not theoretical calculations or simulations but for the outcomes of a true experiment.

Personally I didn't have the opportunity to do such a true experiment but a friend of me, a mathematician who is working on QM, did it and asserts me that, when the screen is very close to the slits there is no more interference!

Have you ever done the experiment by yourself?

Dear Marc,

Your question is very fundamental and leads to an important quantum mechanics concept, the complementarity. In this special case is visibility and which slit concept which play role, and are corresponding to the wave and the particle nature of the light.

The near field gives enough knowledge about the particle feature - which slits the light passes - Let's call it D.

The far field gives information about the wave nature [momentum of light] - if whether they are in phase or out of phase. Let's call this value V.

The sum of "which slit information" and the "visibility" is bounded to unity. The near and far field are both two extreme cases, where for the first case V=0 and D=1 and in the second case V=1 and D=0. Therefore, any intermediate case gives a partial information about "which slit" and the "visibility". Thus, as you know well, the fringes visibility decreases by moving detector plane toward the slits.

Hope that this clarifies some points. By the way, the inequality for visibility and which information is V^2+D^2

The double-slit is THE classical test in optics and QM

I googled and found several sites which answers your question by providing the patterns with changing screen and slit distances

Google

Young double slit demonstrations

Dear Marc,

I also never get opportunity to do such type of experiment as I am working in theoretical part of physics.... but it will really interesting to read further discussion on your question. It will also be useful for me to understand the fundamentals. Thanks for reply...

Dear Ebrahim,

Thank you very much for your answer.

I guess you seem to answer my questions.

If I understand your answer, as the fringes visibility decreases by moving detector plane toward the slits, you confirm that, when the detector plane (i.e., the screen) is very close to the slits it is no more possible to distinguish the fringes. But then what is exactly observed on the screen?

According to your answer the explanation of such a phenomenon would be the complementarity of quantic particles, i.e., the relative impact of the near field, which gives knowledge about the particle feature and of the far field, which gives information about the wave nature. Thus, the near field would be predominant when the screen is very close to the slits: is that correct?

I would be grateful if you could give me some references about it.

The double slit for light can (even) be explained by classical optics as a superposition of EM waves.

Dear Marc,

You have got the point precisely - Herewith please find one of the seminal paper by Englert

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC0QFjAA&url=http%3A%2F%2Fwww.atomwave.org%2Frmparticle%2Fao%2520refs%2Faifm%2520refs%2520sorted%2520by%2520topic%2Fdecoherence%2520refs%2Fenglert%2520visibility.pdf&ei=uxU2UpWmG4G82gXcmYCQBQ&usg=AFQjCNEzoxPflCUEcMDvjKmAHU4GihftAQ&sig2=Fo1dmnHPBrxVrVha5wTnHg&bvm=bv.52164340,d.b2I

Indeed, it is too mathematics and general, and can be applied to very general cases such as the Mach-Zehnder or any dual conjugate variables.

By the way, there are some materials available on the following wikipedia page:

http://en.wikipedia.org/wiki/Englert–Greenberger_duality_relation

Cheers,

Ebrahim

I think it is an embarrassment for a scientists that he can not google or first go to Wikipedia himself

Dear Ebrahim,

I thank you so much for your precious help as I will be able to discuss the point with my friend mathematician.

Cheers,

Marc

My pleasure - good luck!

In double slit whether macroscopic entanglement takes place? If so then accoding to Ebrahim it is for far field?

Study for instance

http://h2physics.org/?cat=48

you notice that the typical ratio of screen-distance to slit-to-slit distance is a factor of 10000, so what distances are you thinking of? Of course when the screen is at the slits the interference patterns is gone because the light must go to one of the slits only

What exactly is your question then?

http://en.wikipedia.org/wiki/Two-slit_experiment

section: Results of the experiment in a simple graphical way

Dear Ebrahim,

I carefully read B-G Englert's seminal paper "Fringe Visibility and Which-Way Information: An Inequality".

I understand the objective of the paper which was "the derivation of an inequality that quantifies duality by stating to which extent partial fringe visibility and partial which-way knowledge are compatible" and thus to study intermediate stages between 'perfect fringe visibility and no which-way information" and "full which-way information and no fringes".

However I don't see that the paper referred to the notion of "near field" versus "far field": am I wrong?

Do you know any papers that speak of this notion specifically? In particular which would apply to Young's experiment?

Ebrahim:

At wikipedia on "Englert–Greenberger_duality_relation" LITERALLY:

The mathematical discussion presented above does not require quantum mechanics at its heart. In particular, the derivation is essentially valid for waves of any sort. With slight modifications to account for the squaring of amplitudes, the derivation could be applied to, for example, sound waves or water waves in a ripple tank.

Dear Marc,

Understood - The two extreme cases that you addressed can be considered as a specific case of the intermediate. However, attached herewith please find a famous article about neutrons - as Harry mentioned, the calculation can be performed classically - which addresses the two extreme cases. Nonetheless, Englret work is a very general and does apply to matter waves such as electrons and neutrons, which cannot be explained with the "classical" mechanics.

Hope that this specifies the issue to Harry as well and the paper could address your thought.

Cheers,

Ebrahim

Setting the screen close to the slits exhibits the particle nature of light, while setting it in the far field exhibits its wave nature. A very cute wave-particle duality experiment.

Charles

I suggested to put the screen directly onto the slits.

Since you are now following this question. do you know where the full treatment is given, taking into account the diffraction at the individual slits and taking into account the finite depth of the slit, this with respect to the visibility of the fringes as a function of distance. I have been searching the web for it.

Charles

In addition, the ratio of the distance to the screen versus distance between slits is a factor of 10000. The very close near field where there is no interference is of the order of 0.1 um, which I assume is barely visible by eye; and in addition there is the diffraction of the individual slits that are typically 0.01 mm or less; this is for visible light.

Sorry Ebrahim, but I don't find that Greenberger & Yasin's paper answers my questioning regarding the near-field versus far-field question.

As Harry seemed to propose me to look at I have found the following in Wikipedia "Double-slit experiment":

"Similar calculations for the near field can be done using the Fresnel diffraction equation. As the plane of observation gets closer to the plane in which the slits are located, the diffraction patterns associated with each slit decrease in size, so that the area in which interference occurs is reduced, and may vanish altogether when there is no overlap in the two diffracted patterns".

If so, as Harry asserted it, the phenomenon, i.e., the disappearance of interferences when setting the screen close to the slits, "does not require quantum mechanics at its heart". What do you think about it?

Marc

The double-slit was the center piece 200 years ago that demonstrated that light is a wave phenomenon. Young did not need quantum mechanics to explain the phenomenon he saw. Actually QM complicates the explanation considerably but does not provide any better explanation after all. The thing is that classical optics works fine in explaining macroscopic phenomena like classical mechanics does.

The two limits you are talking about correspond to Fraunhofer diffraction (far from the slits: http://en.wikipedia.org/wiki/Fraunhofer_diffraction) and Fresnel difraction (close to the slits: http://en.wikipedia.org/wiki/Fresnel_diffraction ) To study the transition between those two, you might want to take a look at: M. Born & E. Wolf; Principles of Optics; 6th Ed.; Cambridge University Press Chapter VIII p. 371.

Oscar

I am restudying Born and Wolf: it is free on the web, but find it quite a difficult book without an initial simpler intro as compared to the other I have as hardcopy (Jenkins and White) and reread a few days ago on this subject. BTW it is not well treated there and on the web I noticed errors in lecture courses for the far field calculations of the fringe distance

Oscar,

Thank you for the information.

Now I think I have the answers to my 2 questions.

Oscar

The entry for Fresnel in Wikipedia is just a series of wave equations and thus absolutely not what it should be in a dictionary meant for those interested with higher education. There must be a site with some illustrations of a phenomenon that occurs with light?!

The equation d sin θ = m λ (for maxima) and d sin θ = (m+1/2) λ ( for minina) are derived in the approximation D >> d, that is the distance from screen to the slits, which is  D, is much greater that the distance between the slits, which is d. (See Resnick and Halliday)

If you want to reduce the distance between the slits and the screen, you can put a convex lens between the screen and the slits. Then the screen can be brought closer to the slits and can be put on the focal plane of the convex lens.

A property of a convex lens is that it will focus parallel rays to a point on the focal plane. Therefore the advantage for us is that we know that light rays meeting at any point on the screen were exactly parallel (not approximately) when they left double slits.

Dear Marc, 

you may find my reformulation of the experiment useful:

https://www.researchgate.net/publication/269400418_A_Theoretical_Reformulation_of_the_Classical_Double_Slit_Interference_Experiment?_iepl%5BviewId%5D=6q5rp5xxSjqt0MnCeLaL1bvx&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BtargetEntityId%5D=PB%3A269400418&_iepl%5BinteractionType%5D=publicationTitle

Article A Theoretical Reformulation of the Classical Double Slit Int...

we did double-slit experiment with the second harmonic of the helical undulator to show the effect of the helical phase. ( harmonic radiation of the helical undulator carries OAM )

https://www.researchgate.net/publication/318620042_Helical_Phase_Structure_of_Radiation_from_an_Electron_in_Circular_Motion