Double slit - why vertical strips?

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  • #1
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Sure - this seams to get asked a lot but I am not entirely getting my head around it.

Why does the double slit provide perfectly vertical interference lines?

I understand the premise of why this would happen in a 2d world - the usual wave analogy applies. However, in 3d it surprises me that the lines continue up and down in a straight line. I imagine the following;
- two Long slots.
- a textbook interference pattern is generated at the screen centre - this relates to light hitting the screen traveling perfectly normal to the screen, slots, and laser.
- at every position up and down the full length of the slots the pattern occurs and we have our vertical interference strips on the screen.

But what happens to say the bottom left and top right slot positions interference with each other? And then every other combination in between? Wouldn't this make the interference pattern have bent ends on every strip rather than being straight lines?
 

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  • #2
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But what happens to say the bottom left and top right slot positions interference with each other?
Your light source is not coherent enough for that. In an ideal world, you would get a single-slit pattern, but in reality your beam has a finite width, some angular spread and so on. if the slits are longer than the beam is wide, you don't get relevant diffraction in that dimension.
 
  • #3
CWatters
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Perhaps google for images. Here are some I found. The ends look curved to me.

two_slits-b.jpg


int-fringes.JPG


http://minerva.union.edu/jonesc/Images/Scientific_Photos/double%20slit%20B%20400px.jpg [Broken]
 
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  • #4
sophiecentaur
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Perhaps google for images. Here are some I found. The ends look curved to me.
The resulting 2D distribution will be approximately the product of the two patterns. It will depend upon the height of the two slots. The reason why the side bars appear shorter will be because of the response of the image sensor, making them appear shorter when they are just at a lower level and the image cuts off sooner. This is the same sort of effect that you get with Litho Film which is used for the old fashioned half tone image production. In that system, the dots in the darker areas are made smaller and the brighter ones are made larger so the amount of ink is proportional to the incident brightness.
If you look at the pattern from a single round hole, you get the Airy's Disc distribution and for two holes you get a pattern that consists of an airy's disc, modulated with vertical stripes.
 
  • #5
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I thought airy's disks where to do with lenses?

Anyway I think I can explain my question a bit better with the sketch below.

The first diagram is the slits viewed from the laser or source. The cross section marked A is the typical textbook cross section. However, the section at B is also providing a wave form on the screen - but since the holes in the slits are effectively further apart (due to the skewed orientation of the approaching wave) the interference position on the screen moves closer to the centre. See the plan view at the bottom. Further when we rotate this image back into the correct alignment it moves the interference even further to the middle. Wouldn't this create an interference pattern more like the middle diagram with curved ends?



image.jpg
 
  • #6
sophiecentaur
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Airy's disc is the diffraction pattern of a circular aperture. You get it with any circular hole - including lenses and microwave dishes even.

The curves on your diagram are presumably what you think is the effect of equal distances from slot to screen? But the interference maxima relate to the path differences from points on the same slot, which is not the same as the total distance.
I wouldn't try to work out the pattern by your non-standard way because of how I learned to do it originally - that is by multiplying the (two dimensional) pattern of a tall slot by the array factor of two slots, side by side. The easiest calculation is the 'far field' pattern that assumes the source (laser or whatever) and the projection screen are far enough from the slots to allow you to be dealing with parallel paths from source to screen. See this wiki link for some ideas about Fraunhofer Diffraction - things are nonintuitive when you try to predict diffraction effects.
 
  • #7
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Single_Slit_Diffraction_(english).svg.png

Single slit diffraction, any way you stack them up they all constructively coincide or not. I wish I could find the 3D electron scattering through molecules it clarifies the point in my opinion.
 
  • #8
sophiecentaur
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View attachment 76602
Single slit diffraction, any way you stack them up they all constructively coincide or not. I wish I could find the 3D electron scattering through molecules it clarifies the point in my opinion.
That example is far too complicated to help with basic diffraction theory. You can solve your problem numerically if you know the dimensions and the wavelength you choose for your electrons but I wouldn't like to do it unless I really had to. ;)
 

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