Diffraction of Light with Moving Slit

[greswd]

If plane waves of light in a vacuum are incident on a slit that is not stationary with respect to the frame of reference, but it is moving either backwards or forwards with a certain speed, what will the diffraction "field" look like?

 

[blue_leaf77]

it is moving either backwards or forwards with a certain speed, what will the diffraction "field" look like?

The diffraction pattern will be either constantly scaled up or down.with time.

 

[greswd]

The diffraction pattern will be either constantly scaled up or down.with time.

what does that mean?

 

[sophiecentaur]

If the motion is just backwards and forwards, the fringes will move from side to side. If the movement is from side to side, the spacing of the fringes will increase of decrease, inversely with the spacing distance.

 

[greswd]

If the motion is just backwards and forwards, the fringes will move from side to side. If the movement is from side to side, the spacing of the fringes will increase of decrease, inversely with the spacing distance.

do you know of any diagram that illustrates this?

 

[sophiecentaur]

do you know of any diagram that illustrates this?

I wouldn't think there would be an explicit description of it anywhere - not like you are asking for. But start with the basic two slit setup and the theory. Moving forward and backwards is just altering the position of the position where the central constructive interference peak will occur and the lateral separation of the slits will give fringes according to the separation. I assume that you already have the basic diagram and theory available to you. Else look in the Hyperphysics pages. Using that information, it is easy to draw a diagram for yourself by superimposing two diagrams onto each other to show the positions of the fringe maxes.

PS I just read your signature quote. Nice one and very apt where dear old Nicola was concerned. He did go loopy after his initial engineering successes.

 

[lychette]

I hope I am correct in understanding this question. Plane waves and a single slit...I think there will be no change in the diffraction 'field'
I think the question is not about 2 slit INTERFERENCE. ...it is about single slit DIFFRACTION ?

 

[blue_leaf77]

If the motion is just backwards and forwards, the fringes will move from side to side.

The intensity pattern formed by a double slit interference is $I(x) \propto \cos^2\left(\frac{\pi d x}{\lambda L}\right)$ for the case of $x$ in the vicinity of the central maximum, so when the screen (or the slit plane) is moving backwards or forward, $L$ is varying, and hence in such a case, won't the whole fringe structure be beating between getting bigger (fringes separation increases when $L$ increases) and getting smaller (fringes separation decreases when $L$ decreases) with the central maximum remains at its place?

 

[greswd]

I'm not concerned about the pattern formed on a screen.

I want to know what the space between the slits and the screen looks like. What the "surface of the water" looks like.

 

[sophiecentaur]

What the "surface of the water" looks like.

Having demonstrated a ripple tank many times, I can tell you that the surface of the water looks just a confusing mess that students (and I) find very hard to interpret. What you actually see is a mass of little diamond shaped peaks and troughs moving from left to right and expanding. The simulation above shows this (once you've sussed out the colour key they use). If you freeze the animation (which you can't do with the water tank) you may see what I mean. Actually, you can sometimes use a strobe to freeze the pattern - but don't rely on it!
With a very wide 'slot', you start to see a central region of identifiable straight line wave fronts where the diffraction pattern is heading towards the 'ray' pattern.

 

[greswd]

But what about with a slit moving with a certain velocity parallel to the plane waves of the water?

 

[Nugatory]

I'm not concerned about the pattern formed on a screen.

I want to know what the space between the slits and the screen looks like. What the "surface of the water" looks like.

They're the same thing. Pick any point on the metaphorical surface of the water. How high will the surface of the water be at that point? It will be as high as the pattern on a screen placed to pass through that point is bright at that point.

 

[sophiecentaur]

But what about with a slit moving with a certain velocity parallel to the plane waves of the water?

Are you looking for some frequency changes where the waves hit the moving edges? As far as I can see, the doppler effect on the waves hitting the edge will be canceled as they leave and the resulting wave wouldn't have a different frequency (well it couldn't, could it?). The wavelets through the middle wouldn't be affected, of course but the path differences would be the same at any instant. (see above comments too). There is the added factor of the 'bow wave' as the slot moves through the water but the waves forming the interference pattern would just sit on top of that.

 

[greswd]

There will be a doppler shift I realized, but not for the waves immediately after the slit. The reason I'm asking this is because I wanted to show that STR is fully compatible with Huygens principle.

Now I've realized that I don't need to use this at all to show that they are compatible.

 

[sophiecentaur]

There will be a doppler shift I realized

I can't see why. The edge of the slit would be moving away from the incident waves and towards the forward propagated waves. (No?)

 

[greswd]

I'll add a diagram. Anyway, Huygens principle is fully compatible with STR right?

 

[sophiecentaur]

"STR"?

 

[greswd]

special theory of relativity

 

[sophiecentaur]

Huygen's principle refers to the medium. If you pass waves through an aperture it would only be the effect at the very edges (waves interacting with the edges) that would contribute to the diffraction pattern. For an infinitely thin slit, the diffraction pattern would be hemispherical and the frequency of the waves would be the same as the source.