Double-slit with movable detector screen

[Physwa]

TL;DR

Double-slit experiment: movable detector screen.

How far back does the “detector screen” have to be from the “double slit” screen for there to be interference?

Greetings. Suppose the “detector screen” is on some kind of movable track that allows very fine adjustments so that you could start with it flush against the “double slit screen” and slowly move it backwards away from that screen at any increment you like. Well, within the limits of current engineering, LOL.

Assume that you are firing a single photon at the double slits. How far away from the double slit does the detector screen have to be before an interference pattern develops on the detector screen?

Is it related to the wavelength of the photon?

 

[PeterDonis]

Assume that you are firing a single photon at the double slits.-

A single photon won't make an interference pattern in the detector screen. It will just make a single dot.

 

[PeroK]

TL;DR Summary: Double-slit experiment: movable detector screen.

How far back does the “detector screen” have to be from the “double slit” screen for there to be interference?

Greetings. Suppose the “detector screen” is on some kind of movable track that allows very fine adjustments so that you could start with it flush against the “double slit screen” and slowly move it backwards away from that screen at any increment you like. Well, within the limits of current engineering, LOL.

Assume that you are firing a single photon at the double slits. How far away from the double slit does the detector screen have to be before an interference pattern develops on the detector screen?

Is it related to the wavelength of the photon?

In principle, there is no minimum distance, but the closer the detection screen the more compressed the pattern. It would be more about the resolution of the detector as to when the fringes are spread out enough to be seen clearly.

 

[Physwa]

A single photon won't make an interference pattern in the detector screen. It will just make a single dot.

When using a single photon, you shoot them repeatedly and the interference pattern emerges over time.

 

[PeterDonis]

When using a single photon, you shoot them repeatedly and the interference pattern emerges over time.

Ok, but that's not what you said. You just said "a single photon", not "lots of photons one at a time".

That said, as far as the interference pattern and your question about it is concerned, it doesn't matter how many photons at a time are inside your experiment. The answer is independent of the intensity of the light source.

 

[Physwa]

In principle, there is no minimum distance, but the closer the detection screen the more compressed the pattern. It would be more about the resolution of the detector as to when the fringes are spread out enough to be seen clearly.

Thanks for the reply!

I assume that the detector wouldn’t be anything special. No higher resolution than what you need for an ordinary experiment where you detect one photon at a time.

Let me make sure I understand your reply. I’m assuming that there would be some distance where you are guaranteed to get no interference because you would know for sure which slit the photon went through. E.g. if the screens were only a micron apart or something. Then there should be another distance where you are guaranteed to get interference because you are simply recreating an ordinary double-slit experiment using a single photon.

So in between those two distances, the bands would slowly emerge, the spread of the photons would slowly increase, as you approach the “guaranteed interference” distance. I think that’s what you are telling me, right?

But at a certain point, the experimenter doesn’t know which slit any photon might have gone through even though interference isn’t guaranteed. They might know that the probability will be higher for one slit over the other based on where the photon hit the screen, but they certainly don’t KNOW which way the photon went.

Would you get “partial interference” at those distances? There are times when the photon might interfere with itself, and then again, it might not?

 

[Physwa]

Ok, but that's not what you said. You just said "a single photon", not "lots of photons one at a time".

That said, as far as the interference pattern and your question about it is concerned, it doesn't matter how many photons at a time are inside your experiment. The answer is independent of the intensity of the light source.

Oh. Sorry about the confusion. Yes, I’m talking about an interference pattern that builds up over time. You use the same frequency of light for an ordinary double slit experiment, but dial down the intensity until you get a single photon.

 

[PeterDonis]

You use the same frequency of light for an ordinary double slit experiment, but dial down the intensity until you get a single photon.

My point is that there is no need to dial down the intensity. The answer to the question of how the interference pattern is affected as you move the detector screen closer to or farther away from the slits is the same regardless of the intensity of the light source. If you wanted to test it experimentally, you wouldn't need to use a very low intensity source with just one photon inside the apparatus at a time, and wait laboriously for interference patterns to build up or not build up over time. You could use a normal high intensity light source and move the detector screen and just watch what happens to the interference pattern in real time.

 

[PeroK]

Thanks for the reply!

I assume that the detector wouldn’t be anything special. No higher resolution than what you need for an ordinary experiment where you detect one photon at a time.

Let me make sure I understand your reply. I’m assuming that there would be some distance where you are guaranteed to get no interference because you would know for sure which slit the photon went through. E.g. if the screens were only a micron apart or something. Then there should be another distance where you are guaranteed to get interference because you are simply recreating an ordinary double-slit experiment using a single photon.

So in between those two distances, the bands would slowly emerge, the spread of the photons would slowly increase, as you approach the “guaranteed interference” distance. I think that’s what you are telling me, right?

But at a certain point, the experimenter doesn’t know which slit any photon might have gone through even though interference isn’t guaranteed. They might know that the probability will be higher for one slit over the other based on where the photon hit the screen, but they certainly don’t KNOW which way the photon went.

Would you get “partial interference” at those distances? There are times when the photon might interfere with itself, and then again, it might not?

It's much simpler than that. If the detector is too close, then various bright and dark fringes will overlap a single detector cell. So, the intensity will be averaged out.

Ideally, the detector needs to be a distance that is significantly greater than the size of the slits and the gap between them.

 

[Physwa]

My point is that there is no need to dial down the intensity. The answer to the question of how the interference pattern is affected as you move the detector screen closer to or farther away from the slits is the same regardless of the intensity of the light source. If you wanted to test it experimentally, you wouldn't need to use a very low intensity source with just one photon inside the apparatus at a time, and wait laboriously for interference patterns to build up or not build up over time. You could use a normal high intensity light source and move the detector screen and just watch what happens to the interference pattern in real time.

Fair enough.

I’m just curious as to what happens at those “intermediate stages,” so to speak.

 

[PeterDonis]

I’m just curious as to what happens at those “intermediate stages,” so to speak.

Yes, but they are "intermediate stages" regardless of the intensity of the light source. Whatever is there, you don't need to have a one photon at a time source to see it.

 

[Physwa]

It's much simpler than that. If the detector is too close, then various bright and dark fringes will overlap a single detector cell. So, the intensity will be averaged out.

Ideally, the detector needs to be a distance that is significantly greater than the size of the slits and the gap between them.

Huh. I had assumed that the detector screen was using some sort of a photoemulsion that reacts no matter where the light hits it. That you would not need a "detector cell."

 

[PeroK]

Huh. I had assumed that the detector screen was using some sort of a photoemulsion that reacts no matter where the light hits it. That you would not need a "detector cell."

Every detector will have a finite resolution.

In any case, the slits can't be perfect point sources. You are going to get experimental error on the pattern if the screen is too close.

I don't see what any of this achieves.

 

[Physwa]

Every detector will have a finite resolution.

In any case, the slits can't be perfect point sources. You are going to get experimental error on the pattern if the screen is too close.

I don't see what any of this achieves.

Well, I think the Hitachi people used a photographic plate when they reproduced the effect with single electrons. They seemed to have a pretty high resolution.

https://pioneerworks.org/broadcast/picture-this-double-slit-test

As to what it achieves…well, it would satisfy my curiosity. If I could actually get the question answered, LOL!

 

[renormalize]

If I could actually get the question answered, LOL!

Have you put any effort into researching the answer for yourself?
From: https://en.wikipedia.org/wiki/Double-slit_experiment I quote:
"Similar calculations for the near field can be made by applying the Fresnel diffraction equation, which implies that 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.[81]"
Reference [81] is: Longhurst RS, Physical and Geometrical Optics, 1967, 2nd Edition, Longmans.

 

[Physwa]

Have you put any effort into researching the answer for yourself?

From my point of view, there is no need to get involved here if you think certain questions don’t deserve an answer. No matter the rationale.

From: https://en.wikipedia.org/wiki/Double-slit_experiment I quote:
"Similar calculations for the near field can be made by applying the Fresnel diffraction equation, which implies that 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.[81]"
Reference [81] is: Longhurst RS, Physical and Geometrical Optics, 1967, 2nd Edition, Longmans.

I never noticed that paragraph in the wiki, thanks for the reference.

Of course I knew that the interference pattern disappears eventually, even though in the wiki they only say that it ‘may’ disappear.

But I was wondering if there was a known distance that the pattern would absolutely disappear, perhaps depending on the wavelength of the light used or some such.