Double slit - why do we get an interference pattern?

[Emissive]

In a standard 2 slit experiment setup when the interference pattern is visible - if the screen is moved forward the pattern must 'move' across the screen as the alignment of wave peaks and troughs change. I.e if we start with an intense band at the centre then move the screen forward half the wavelength of the light frequency then this constructive interference will become destructive and we should get a dark spot - is that correct?

So why do we get the pattern at all? If we are using a laser as the light source then photons will be emitted at differing distances from source - their wavelengths commencing at random points in the gain medium - meaning the alignment of each of the light waves will be effectively random - thereby leaving no interference?

 

[nasu]

I.e if we start with an intense band at the centre then move the screen forward half the wavelength of the light frequency then this constructive interference will become destructive and we should get a dark spot - is that correct?

Why would you think this?
If you move the screen along the direction perpendicular to the plane of the slits only the distance between the bright spots will change.
Maybe you have something else in mind and I misunderstood your description?

 

[jtbell]

if we start with an intense band at the centre then move the screen forward half the wavelength of the light frequency then this constructive interference will become destructive and we should get a dark spot - is that correct?

No. What matters is the difference between the path lengths from the two slits to the point on the screen that you are looking at. At the center of the screen (more precisely the point that is directly "opposite" the slits), the two path lengths are equal regardless of the location of the screen, so you always have constructive interference there.

 

[Emissive]

So that typical diagram of waves going through the slots is not entirely correct? It is only correct for that one screen position?

(The one where arcs representing wave peaks radiate from each hole and the amount of interference on the screen is given by the two creasts overlapping). On this diagram if the screen is moved forward we would be in trough moving the pattern across the screen.

I thought the spacing between arcs was representative of the light wave length? So using a higher frequency would bring the interference lines closer together?

 

[nasu]

I am afraid you are misinterpreting that pattern. It si not the interference pattern but a snapshot of the phase of the waves at a given time.
The important thing is that right in the middle you have the two waves in phase. That means they go through a maximum (crest), a minimum or anything in between at the same time.
If that pattern shows crest in some point, at the instant for which the snapshot was taken, a little latter (half a period) the waves will have a minimum at the same point. And this without moving the screen.

 

[Emissive]

Yeap - definitely was!

I think i now see now why the sum of the amplitudes can be taken from the centre wave because your interested in the directionality of the two vectors.

But... I think the second part of my first question still stands...(or at least you can correct me on this too!)

If the photon emitter is a laser then the gain medium has depth - wouldn't this create photons effectively of random phase when they pass the laser lens? If so then as they pass through the slots they will also be random phase and therefore not provide the interference pattern?

 

[Emissive]

Actually - after a little more thought - why bother moving the waves over time? If your interested in the coherence of the waves we could much more easily image the waves as standing wave with its propagation over time...perhaps that's a side question!

 

[mrspeedybob]

If the photon emitter is a laser then the gain medium has depth - wouldn't this create photons effectively of random phase when they pass the laser lens? If so then as they pass through the slots they will also be random phase and therefore not provide the interference pattern?

No. Lasers produce coherent light. All the photons are in phase with each other. Even if they weren't though you would still get an interference pattern because the photons do not interfere with each other, each photon interferes with itself (more precisely the probability amplitudes interfere). You get the same interference pattern if the photons go 1 at a time.

 

[Emissive]

Interesting - thanks.

But surely if the lasers light was of incoherent phase each photon would display the interference pattern (but being a individual we would only see it in one location) - other photons would be out of phase so we might expect after many photons a strip of light with no visible pattern?

 

[mrspeedybob]

Nope. Each individual photon is detected at a specific point. There is no way any sort of pattern can be determined from a single photon. After many photons pass through the apparatus you see stripes on the film where many photons have hit and stripes where few or no photons have hit, that is the interference pattern.

It makes no sense as long as you think of photons as tiny little particles like extremely small specks of dust. They are not. A particle like a speck of dust must exist in a specific place, a photon (or any quantum particle) exists simultaneously in a range of locations, like a field, until it interacts with another quantum particle such as an electron on a photographic film. This interaction consumes all of the energy of the photon, hence it can only interact once, in one location, despite the fact that it's existence was diffuse before the interaction.

In the case of a double slit experiment a single photon travels through both slits simultaneously and proceeds to interfere with itself resulting in regions where it is very unlikely to interact with another particle and regions where it is likely to interact.