Talk:Diffraction

I added a derivation of single-slit diffraction. I will add the N-slit derivation later, after some order is imposed on this page. Perhaps a TOC?

 - SNH

Hold on one minute. I'll be the first to admit I know very little more about diffraction above what you learn in a standard Phys with Calc course, but I've got two issues with this page.

First off, the picture of water waves impinging on double slits is not really an example of diffraction. It's an example of entirely different wave phenomena called interference. Diffraction is what happens when the wave hits the slit. After that, diffraction is over and what you see is the interference between two point wave sources. Interference, not diffraction. Or am I going crazy?

Secondly, I have a few issues with the single slit diffraction intensity derivation. The derivation explicitly says that unprimed coordinates "x" label slit points, and that primed coordinates "x'" label the target points. This is backwards from standard notation (ie- Jackson, Griffiths, Panofsky and Phillips, etc). Usually, primed coordinates label the source point (ie- the slit here) and unprimed coordinates label field points (ie- the target here). But never mind that. A good physicist is flexible (but I still think we should follow standard notation for pedagogical reasons).

But never mind that. With this convention, we want to integrate dslit, meaning, we want to integrate over dx dy, and the resulting function should be a function of x'. From the stated convention, the resulting function which should describe intensity on the screen should be a function of x'.

However, the derivation then integrates over x' and y'. The function that describes intensity at the target is a function of x. This is completely backwards from the stated convention that x' labels the target and x labels the slit.

The derivation is a mess. I'm not going to change it just in case somebody slipped LSD into my morning coffee, and I'm totally way off base on this. In case I'm not way off base, I recommend changing:

"We will assume that the slit is infinitely thin in the z direction, so dslit = dxdy. Take the center of the slit to be at x and the wave hits its target at x'."

To:

"We will assume that the slit is infinitely thin in the z' direction, so dslit = dx'dy'. Take the center of the slit to be at x' and the wave hits its target at x."

  --Sliver

I agree with many of your points, Silver but have a few points of contention. First, diffraction is correctly defined on the page and is the same phenomenon in water waves as in EM waves and particle waves. Interference is caused by differring peaks and troughs in the diffracted wave, due to differing path lengths to a given screen from different slits. In other words, diffraction and interference are related phenomena. Referring to interference on a page about diffraction conforms to common usage (see Nobel prize lectures in 1914, 1915, 1937 and 1994 in physics, 1936, 1962, 1964 in Chemistry). However, a good argument can be made that the two pages should be better cross-referenced.

I appreciate the note on my mixing up prime and un-primed frame. However, I was consistent. To get a function in terms of unprimed x, we need to integrate over primed x. If x-prime is the source with width a, then integrating over the slit will go from -a/2 to a/2 and yield a function in terms of unprimed x. I've made your suggested change at the outset of the derivation.

Could you be more specific about which part of the derivation is a mess? Any suggestions on how we can improve it?

--SNH

Re the water waves, in my opinion SNH is correct and Sliver is incorrect. The example with the water waves is diffraction, and is exactly analogous to double-slit diffraction of light waves (except that light has two modes of polarization). Both cases are also examples of interference. Interference is the reason diffraction occurs. Diffraction is one type of interference. You can take my opinion with a grain of salt, since I wrote the water wave stuff in the first place. --Bcrowell 22:50, 28 Feb 2005 (UTC)

Hecht's "Optics" says that there is no real distinction between interference and diffraction, but the term "interference" is customary when talking about only a few waves and "diffraction" when talking about a large number of waves. As far as I've seen, the double slit example is universally described as "diffraction", although it would also be accurate to call it "interference". Also we're not talking about point sources; the slits have finite width. Pfalstad 23:37, 28 Feb 2005 (UTC)

Re the x, x', dx', etc., if the center of the slit is at x', then x' is a constant, not a variable, and there can't be any dx'. We really have three different values of x: the x at the center of the slit, the x where the final intensity pattern occurs, and the x at which we're integrating the wave. It seems simplest to me to define x=0 to be at the center of the slit, in which case we can cut it down to two variables. I'm going to go ahead and change it to be that way. --Bcrowell 23:45, 28 Feb 2005 (UTC)

I've gone through the derivation and tried to fix things that seemed broken. I'm not sure to what extent my changes will address what SNH didn't like, but maybe we're converging. --Bcrowell 00:41, 1 Mar 2005 (UTC)

Re: Primed and Unprimed

I think that there may be some confusion on the primed and unprimed variables and what they represent. The surface into which the slits are cut is a plane defined by (x', y', z') where z'=0 because the slit is infinitely thin. These define a coordinate system rather than precise points. In this manner, the waves originate at (0,0,0) rather than (x',y',0). In fact, I have made an assumption (not stated...my fault) than x=0 when integrating from -a/2 to a/2 over the slit. When the wave hits a second plane defined by (x, y, z)--where z is unimportant because we are measuring point density -- the consequence of assuming the originating slit is of infinite height (integrating from y=-&inf; to y=&inf;) is that the diffraction pattern (on the unprime plane) also has infinite height.

So perhaps the lead-in paragraph should read:

Let the slit lie in the unprimed x-y plane with infinite height in the y direction and width a in the x direction. Consider an infinite number of particles passing through this slit. Let the screen on which the diffraction pattern is projected by a distance z' away from the origin and the diffraction pattern be represented by the plane (x', y').

--S.N. Hillbrand 14:00, 1 Mar 2005 (UTC)

Bcrowell, the picture that's used to display "two slit diffraction" is misleading and used incorrectly. Pfalstad is correct when he says that it's customary to call interference of a few waves (typically two) "interference" and interference by an infinite or nearly infinite number of waves "diffraction". Interference is very simple, both conceptually and mathematically. Diffraction, the effect of many interferences, is very difficult. The two slit picture we use is a great demonstration of interference. It's a misleading (at best) demonstration of diffraction. These are my references to back up that claim:

• Richard Feynman: Feynman Lectures (Addison Wesley), vol I pg 37-3. He has the same diagram as an example of "interference".
• Susan Lea, John Burke: Physics, the Nature of Things (Brooks Cole), pg 567. Again, interference, not diffraction.
• Lerner, Trig: Encyclopedia Of Physics, 2nd Ed (VCH), pg 634. Interference, not diffraction.
• Halliday, Resnick: Fundamentals Of Physics, 7th ed (Wiley), pg 964-965. Picture in Interference chap, not Diffraction chap.

The list goes on and on. I've heard of "Young's two slit interference experiment". I've never heard of "Young's two slit diffraction experiment". If you don't like my references, go here: http://images.google.com/ and do an image search on "interference". Then do an image search on "diffraction". Compare the two groups of pictures.

There are SO many great pictures of diffraction out there. Pictures that nobody in their right mind would look at and say "Huh?" to. Why use this one which, at worst is wrong but at best is confusing? Suggestion:

Remove the image of the two-slit water wave interference. It belongs on the interference page, not the diffraction page. Replace that picture with a good, solid picture of diffraction, like:

  * A GREAT instructional picture:  http://www.gcsescience.com/pwav37.htm
  * This is a canonical picture of diffraction: 
  * Nice demonstration of diffraction by EM waves and matter waves:  

The gcsescience picture is excellent; it's unmistakable diffraction. I'll do the legwork to get permission to use the picture if other people like it. I could even draw my own version of the pictures if we can't secure permission. I'm pretty hand with The Gimp, and Flash.

As for the derivation, it's perfect now. The prime/unprime question was completely resolved and it follows Jackson's convention, which is always a good thing. Thanks!  :)

--Sliver

Hmm... I think that Pfalstad has hit the nail on the head that diffraction and interference are often used interchangably. Sliver, please reference your copy of Feynman's Lectures, Chapter 30-1 (Diffraction). To quote:

This chapter is a direct continuation of the previous one, although the name has been changed from Interference to Diffraction. No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them.

So, in this spirit, perhaps a link to the interference page would be appropriate along with a note explaining the confusing usage.

--S.N. Hillbrand 17:38, 2 Mar 2005 (UTC)

My dictionary says, "diffraction: modification of the behavior of light or of other waves resulting from limitation of their lateral extent, as by an obstacle or aperture," and "interference: the phenomenon of two or more waves of the same frequency combining to form a wave in which the disturbance at any point is the algebraic or vector sum of the disturbances due to the interfering waves at that point." This means that all diffraction is interference, but not all interference is diffraction. The water wave example is an example of diffraction, and therefore of interference as well. If I have two speakers broadcasting sine waves in phase with each other, then that's an example of interference, but not diffraction (because there's no obstacle or aperture). If you do a google search on "double slit," the first screenful of results includes both "double-slit interference" and "double-slit diffraction." Double-slit diffraction happens to be the simplest example of diffraction, so that's why it's appropriate to lead off the article with it. A real 2-d diffraction photo with no legal problems would be great to see later in the article, once the reader has been prepared to understand the basics of the phenomenon; a fake one would, IMO, not add anything to the article (and would also be difficult to do right). --Bcrowell 21:58, 2 Mar 2005 (UTC)

I think it would be great to have at least one 2-d diffraction image in the particle. The razor blade image would be perfect. The GCSE physics images get the message across, but they lower image isn't very accurate; there would be a lot of diffraction in that case. The aperture isn't nearly wide enough compared to the wavelength to make it look that neat and tidy. Pfalstad

I just finished writing an n-slit derivation for the page. I never liked the phasor method derivation, so I've stayed clear of that. Hopefully this way is a clear explanation and follows naturally from the single-slit case. 00:55, 6 Mar 2005 (UTC)

Hi Hillbrand -- Why did you delete all my new introductory material? If you're going to delete such a big chunk, it would make sense to say what you're doing in the edit summary, and discuss your reasons on the talk page. --Bcrowell 03:03, 6 Mar 2005 (UTC)

Mmm...I just noticed two other edits of mine that you reverted without explanation: the deletion of the Newton's rings stuff (which is not diffraction, as noted in my original edit summary), and the uniting of the two separate discussions of diffraction of particles. Again, please don't do huge reverts like that without explanation, please give accurate edit summaries, and please discuss things here. --Bcrowell 03:31, 6 Mar 2005 (UTC)

Bcrowell- my sincere apologies. I did not mean to revert any of your work. I must have posted an older version, although I could have sworn I grabbed the most receent version before posting the new material. But page histories do not lie, I suppose. I'll be more careful in the future. S.N. Hillbrand 04:55, 6 Mar 2005 (UTC)

Oh, I see -- no problem. Thanks for explaining. :-) --Bcrowell 15:43, 6 Mar 2005 (UTC)

Style issues

According to the Wikipedia:Manual of Style, the section headins must not have many capitals. So, things like

==See Also==

should be

== See also==

This article needs to be edited to confirm to the style. Thank you. Oleg Alexandrov 04:52, 9 Apr 2005 (UTC)

Go ahead. No need to ask first.--Bcrowell 15:31, 9 Apr 2005 (UTC)

I hope I can get to it today. Oleg Alexandrov 17:11, 9 Apr 2005 (UTC)