Question about single slit diffraction .

[Firefox123]

question about single slit diffraction...

Hey all...

I am trying to get a deeper and more intuitive understanding of single slit diffraction from a physical perspective.

I have already read the general explanation from back when I was an undergrad in my physics classes...since then I have read some explanations on the web, but these usually focus more on the math and the general principle rather than a physical picture or description of what exactly is happening at the edges of the slit.

The wave is obviously deflected or bent in such a manner that it ends up interfering with itself...but I am having a diffcult time picturing it.

With water waves...I can almost picture a "molecule" being "deflected" at an angle by the edge of the slit and this happening at both the top and bottom of the slit creating waves that end up combining and interfering with other parts of the same wave...like the middle portion in the center of the slit.

But I could be completely off here in my attempt to have an intuitive picture and feel for what is happening.

I am trying to get a better grasp of waves in general...and specifically to increase my understanding of electromagnetic waves. But to do that I should have a better grasp, both mathematically and physically, on the topic of waves in general. So here I am looking for more for a physical answer or one that I can mentally picture.

Can anyone help me here? Maybe a quick explanation or a link to a website with a good description or picture? I have looked now for several days and can't find what I am after.

Thanks in advance for any assistance.



Russ

 

[Doc Al]

I find it useful not to think of single slit diffraction as an "edge effect". Instead, consider the wave front passing through the slit as a set of small elements. Treat each element as a point source (Huygen's principle), then consider how these "point sources" interfere.

A site you may find helpful is: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html#c1

 

[Firefox123]

Hey there Doc Al...

Thanks for the reply.

I find it useful not to think of single slit diffraction as an "edge effect". Instead, consider the wave front passing through the slit as a set of small elements. Treat each element as a point source (Huygen's principle), then consider how these "point sources" interfere.

A site you may find helpful is: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html#c1

Yeah...using Huygens principle is very useful for thinking about diffraction and the hyperphysics site is a good link...

I am trying to get around having to use Huygens principle here though...

Is there another way to think about this issue? Is there a way to look at it as an "edge effect"? I realize an "edge effect" explanation might get troublesome when looking at light comapred to, say, a water wave...but can we look at the phenomenon from that perspective?

Also...how did Huygens come up with his principle? It seems to be useful...but how am I to think of it physically? Is it a valid physical description of what is happening in a water wave or a light wave? Or is it just a mathematical tool or mental picture that doesn't necessarily correspond to what is happening physically?

Im trying to "picture" why the wave forms an interference pattern after encountering the slit.

Not trying to be difficult here...just struggling with things I don't fully understand.



Russ

 

[jtbell]

Also...how did Huygens come up with his principle? It seems to be useful...but how am I to think of it physically?

Put your fingertip into a still surface of water, and move it up and down. You get waves spreading out in circular ripples from that point. But only those water molecules that are right next to your finger, "know" about your finger directly. Water molecules some distance away can respond only to the motion of the molecules that are "right next" to them. This is a characteristic of all wave motion. The motion of the wave at each point is directly "caused" only by the motion at adjacent points.

Therefore, if the water at any point is oscillating up and down, it seems plausible to me that you can consider it as a source of circular ripples, regardless of whether there is any external source at that point or not.

 

[Firefox123]

Hey there jtbell...

Put your fingertip into a still surface of water, and move it up and down. You get waves spreading out in circular ripples from that point. But only those water molecules that are right next to your finger, "know" about your finger directly. Water molecules some distance away can respond only to the motion of the molecules that are "right next" to them. This is a characteristic of all wave motion. The motion of the wave at each point is directly "caused" only by the motion at adjacent points.

Therefore, if the water at any point is oscillating up and down, it seems plausible to me that you can consider it as a source of circular ripples, regardless of whether there is any external source at that point or not.

This explanation seems to work well for water waves, since we can think of the wave in terms of molecules moving around...so I can picture a single molecule affecting every other molecule that is "close" to it by its motion...

I get a picture of a single "up ad down" moving molecule pulling and pushing on several other molecules...some directly in front of it and others at various angles...thus producing the circular ripples you referred to.

So as far as water waves go...the Huygens principle seems to make physical sense in an intutive way and is useful for giving me a picture of what happens in single slit diffraction.

Thanks for the answer

So how do I extend the above discussion to light waves?

And is it possible to think of diffraction from an intutive/physical perspective without relying on Huygens principle?

not that I have anything against Huygen...I just like to try and look at things using several different approaches...I find I get a deeper understanding when I do that...



Russ

 

[jtbell]

So how do I extend the above discussion to light waves?

It seems to me that what you're reallly asking is, "What is the real physics underlying electric and magnetic fields, and electromagnetic waves?"

From a classical point of view, there is no generally accepted answer to that question. There are a bunch of people with Web sites who are trying to sell "aether theories" which involve an all-pervading medium whose motions are the real basis for electromagnetic waves. But no real physicist has taken such theories seriously for almost a century now, as far as I know. At the classical level, we simply take Maxwell's equations and the electromagnetic force law as initial postulates, on the same level as Newton's laws of motion.

From a quantum theoretical point of view, I suppose it might be possible to "explain" diffraction of light using real photons for the light itself and virtual photons emitted by the walls of the slit; but I have no idea of what the details would look like. It would surely be messy. And then there's the question of how "real" virtual photons are, anyway. I suspect that most people who aren't happy about the "reality" of E and B fields aren't going to be very happy about quantum electrodynamics, either.

 

[Firefox123]

Hey there jtbell...

Sorry for the delayed response...I am an Army Reservist currently serving in Kuwait...so sometimes I can't respond right away...

It seems to me that what you're reallly asking is, "What is the real physics underlying electric and magnetic fields, and electromagnetic waves?"

Well...the question wasnt necessarily intended to go down that path...I just wanted to see if there was another physical approach to single slit diffraction besides employing Huygens principle.

I like having various ways of looking at stuff...both mathematically and physically...

From a classical point of view, there is no generally accepted answer to that question. There are a bunch of people with Web sites who are trying to sell "aether theories" which involve an all-pervading medium whose motions are the real basis for electromagnetic waves. But no real physicist has taken such theories seriously for almost a century now, as far as I know. At the classical level, we simply take Maxwell's equations and the electromagnetic force law as initial postulates, on the same level as Newton's laws of motion.

I haven't looked too much at any current aether theories...Im planning on taking a closer look at the theory of loop quantum gravity in the near future (I also want to study string theory as well)...I say that because I like the idea that perhaps space-time itself is quantized and I sometimes imagine that the "particles" that carry EM waves are space-time itself...

From a quantum theoretical point of view, I suppose it might be possible to "explain" diffraction of light using real photons for the light itself and virtual photons emitted by the walls of the slit; but I have no idea of what the details would look like. It would surely be messy. And then there's the question of how "real" virtual photons are, anyway. I suspect that most people who aren't happy about the "reality" of E and B fields aren't going to be very happy about quantum electrodynamics, either.

When you say "the walls of the slit" are you thinking of the edges specifically or the entire width of the slit or something else?

Im not expecting anyone to explain what E and B fields "really are" or what anything, for that matter, "really is" since ultimately we get into the weirdness of quantum and in the end we really don't know what the exact nature of nature itself is...

My background is in EE (I have a BS in EE from Penn State) and I have only recently begun to work on my masters...so my knowledge of math, physics, and engineering is at the very basic level, I am afraid. In grad school I am focusing on antennas and radar and the like (since I am very interested in it and its what I do at work anyway) but I don't have as much practise working with Maxwells equations, and indeed with waves in general, as I would like.

My knowledge of quantum physics and relativity theory is even weaker...but I do know enough about these topics to not expect anyone to know what E and B fields "really are".

Besides...math, physics, and engineering wouldn't be any fun if they were too easy.




Russ

 

[rayjohn01]

The edge effect is a red herring -- there are two ways of viewing this experiment,from classical wave theory or quantum mechanics both yield a measureably good answer.
The latter is hard to see because it involves the 'uncertainty principle' in which you cannot constrain the size of something without effecting it's momentum ( the slit is a constrainer of where a photon can be ) it reponds by changing where it goes in statistical fashion if you fire photons one at a time -- they still form a pattern.
The Hygens principle assumes a LOT of photons and how they behave on average
and is a model of how transverse waves behave meeting a barrier.
Although water waves yield similar results , at a detailed level electromagnetic waves do not depend upon a media nor do they jostle each other and an accurate treatment ( as someone already said ) requires to solve Maxwells equations for the bounding surfaces to the electromagnetic field. This is simply NOT easy to visualize -- if you look at Microwave conducting tubes you will see there are many different 'modes ' of conduction which are solved on computers.
In a sense the Hygens concept is probably about as close to getting a visual solution
as you are likely to get -- the rest is applied maths.
I would recommend reading a simple quantum explanation -- there is a VERY important concept here NOT covered by field theory -- and which makes this experiment one of the breakthroughs in modern physics.
Because light is emitted by atoms in mostly random fashion , it is deemed impossible for light from different atoms to form an interference pattern , as their starting times (wave phase) is continually changing !
The result is that it seems that ONE photon must interfere with itself ! That is an energy bundle which can be observed to arrive at a screen ONE at a TIME -- must have traveled both paths ---- This is the essential point to slit experiments and has been called THE GREATEST MYSTERY in PHysics.
Although I am ultimately talking about the double slit it is really the same thing
since any slit can be considered as being made of strips of space.
Yours Ray.