Fringes in a One Slit Experiment with a water tank

[DaTario]

Hello All,

I would like to know why it´s so difficult to find information about the generation of fringes in a one slit interference experiment in a water tank.

Best Regards,
DaTario

 

[Dale]

It is usually called "diffraction" instead of "single slit interference". Try searching for that instead.

 

[DaTario]

Sorry, Dale, for not making myself clear enough. I am referring to the single slit intereference pattern in a Fraunhhoffer set up, in which one sees those fringes (easily seen when using a laser source, for instance). In searching for diffraction, on the other hand, I usually get experiments in water tanks where the wave front simply gets curved, with a circular shape, but the fringes one obtains by applying Huygens principle and interference principle are not present.

 

[sophiecentaur]

Sorry, Dale, for not making myself clear enough. I am referring to the single slit intereference pattern in a Fraunhhoffer set up, in which one sees those fringes (easily seen when using a laser source, for instance). In searching for diffraction, on the other hand, I usually get experiments in water tanks where the wave front simply gets curved, with a circular shape, but the fringes one obtains by applying Huygens principle and interference principle are not present.

The curvature is because of the 'average' time taken for each wave front to travel from the source and that's something that you won't see with a beam of light, because the phase is very much less obvious. The diffraction pattern that can be observed with light shows the mean energy flow in different directions but, using a piece of string of a given length, you could (in principle) plot the locus of equal phases of the light from the source. That would, of course, be curved and the same shape whatever the wavelength you were using.
I have a pet hate of ripple tanks because the message they give is confusing and the quality of the patterns can often be not that good (certainly with the sort of ripple tank demo that's given in UK schools).
"but the fringes one obtains by applying Huygens principle and interference principle are not present". If you do the full Huygens analysis you get exactly the right answer but, rather than having just one source at each slit in a simple multi slit demonstration, you need an infinite number of sources across a single slit (diffraction, as Dale wrote above). You need to Integrate the effect over the width of the slit.

 

[Dadface]

 

[sophiecentaur]

@Dadface : Those are very nice images but what do they actually show? For a start, they are very near field so they are not Fraunhoffer region because the approximations used in that analysis really do not apply. The patterns are only a few slit widths in extent and the dominant visible features are more related to the drop off in wave energy and transit time than the maxes and mins of the pattern. I would be interested what students would actually have to say if they were asked to describe what they have learned about what is going on and how it relates to the typical diffraction and interference patterns with light.
The OP needs to search with the term Fresnel Interference, which describes the near field. I am not too surprised that the returns on such a search are more aimed at radio wave and light diffraction because there is probably more interest in those fields. Surface / gravity waves are a bit of a minority interest.

 

[Dadface]

To me the images show quite clearly the single slit diffraction pattern one would expect with waves in a ripple tank. In each case there is a central maximum dropping to a minima on each side. The width of the pattern is seen to increase as the width of the gap decreases and subsidiary maxima can also be seen. These show up particularly clearly in diagrams b.

 

[Dale]

I am referring to the single slit intereference pattern in a Fraunhhoffer set up

Since Fraunhofer is a far field approximation I wouldn't expect to see it in typical ripple tanks. Lasers have a shorter wavelength and better coherence, so far field effects are easier to set up

the fringes one obtains by applying Huygens principle and interference principle are not present

I disagree. The left column of images posted by @Dadface is a good example

 

[sophiecentaur]

To me the images show quite clearly the single slit diffraction pattern one would expect with waves in a ripple tank

Yes. Excellent, in a qualitative way but the rounded off shape of the pattern and the fact that wave amplitude drops off so fast detract from the basic message. You can see a side fringe, either side of the main beam best in the second in from the right and the second in from the left. However, the very basics of diffraction that tell you the pattern from a wide aperture is narrower than from a narrower aperture are not clear because the 'throw' of the beam is so short. In fact, one could easily get it the other way round if not actually instructed about what to see.
Imo, diffraction basics are far better demonstrated with microwaves or ultrasound, where the signal actually makes it as far as the Fraunhoffer region.

 

[DaTario]

I am very happy to see figure b of Dadface. Thank you. In fact I just happen to observe a similar photo in French´s book Oscilations and Waves.
So we must conclude that even in the near field it is just a matter of setting up the parameters correctly (lambda and the slit aperture) in order to observe the interference fringes due to diffraction in water.

Thank you all,

Best wishes,
DaTario

 

[sophiecentaur]

“Just a matter” The calculation is straightforward but you have to use the near field version. But the distribution of field (illumination or wave height etc.) over the aperture needs to be characterized.

 

[DaTario]

“Just a matter” The calculation is straightforward but you have to use the near field version. But the distribution of field (illumination or wave height etc.) over the aperture needs to be characterized.

Are you saying that the near field version is the most convenient theoretical approach for waves in water, are you?
If yes, Ok, I got it.
OBS: In my post #10, I was referring to the experimental set up exclusively and what is needed to provide a clear observation of the fringes (a correct adjust of lambda and the slit aperture). Of course there are other variables like the viscosity of the fluid in the tank, the amplitude of the incident waves, but the most important seems to be the wave length and the slit aperture.
DaTario

 

[sophiecentaur]

Are you saying that the near field version is the most convenient theoretical approach for waves in water, are you?

Near field applies to near field. If you draw a triangle from the edges of the aperture to the point of interest and the angle between the long sides is significant then you can't use the far field assumption that they are parallel. This is true for any type of wave and it really isn't "convenient". It's a real pain in the butt to do the analysis but you can't do without it.

 

[DaTario]

Near field applies to near field. If you draw a triangle from the edges of the aperture to the point of interest and the angle between the long sides is significant then you can't use the far field assumption that they are parallel. This is true for any type of wave and it really isn't "convenient". It's a real pain in the butt to do the analysis but you can't do without it.

Ok. Your comment is consistent with my previous understanding of this theoretical part. In fact, it was the experimental possibility (or impossibility) of building the fringes with waves in water that lead me to formulate the OP. Thank you.

 

[sophiecentaur]

You could certainly get a 'fair' agreement between the angle you measure between the directions of the first nulls and the width of the slit in wavelengths. That would be one step better than just 'narrow gives wide beam and wide gives narrow'.
It's not too difficult to use a numerical approach rather than using the analytical formulae; treating the problem as Interference from a large number of closely spaced sources. You can do a calculation along the lines of huygens, adding the phasor contributions from a number of, say ten locations (wavelets) along the source line and working out the path distances to various points on a 'screen' from each source point. There are many sources of how to do this but this one gives the approach. It's convenient to do this sort of thing with a spreadsheet if you don't find coding a complete program or app. At one time, I used to do this sort of thing for simple situations using Excel but I don't have the files any more.
If you have a ripple tank available, you can compare the wide single slit pattern with the patterns from two points, spaced by half the slit width.

 

[DaTario]

Ok, thank you very much.

DaTario