[hamdani yusuf (OP)]

When monochromatic light passes through a single slit and produces a pattern on a screen.  What do you call that pattern on the screen?

Interference pattern caused by diffraction.
In reflection mode, a single slit aperture which is made of reflective material also produces interference pattern. But this time, it doesn't involve diffraction.

When monochromatic light passes through two slits and produces a pattern.... What do you call that?

When ...light  ... passes.... diffraction grating... screen.  What do you call that?

Same as above answer.

[hamdani yusuf (OP)]

My view is... what the figgy pudding does it matter?

Does it matter if interference patterns in the cases of Lloyd's mirror and thin film interference are called reflection patterns instead?

[hamdani yusuf (OP)]

I have a delightfully disgusting story about x-ray diffraction which can wait for another day.

I can't wait to learn from your experience.

[hamdani yusuf (OP)]

Here's the more geometric interpretation using rays of light, which I'm sure you've seen before:

The middle light beam seems to deflect for no obvious reason, which doesn't seem reasonable and suspiciously misleading. Will it behave the same way if the top and bottom obstacles are removed?

[Eternal Student]

Hi.

   Alancalverd and Hamdani Yusuf have asked similar things...

The middle light beam seems to deflect for no obvious reason, which doesn't seem reasonable and suspiciously misleading.

and,

But most mysterious of all, the one in the middle also turns left for no reason at all!

   I can't help but feel that you have misunderstood the Huygens-Fresnel principle.   The centre of the aperture isn't having just one beam of light sent away from it.   Neither is the left edge or right edge of the aperture.   Every point on the wavefront is a source of secondary spherical wavelets.   It's "spherical" as in light rays are sent in all directions.   This diagram may help:



   Imagine the centre of that diagram is the centre of the aperture.   The red circles indicate peaks in the wave,  so any red circle is what can be called a wavefront.   The wave spreads out from the secondary source like this... in a spherical manner.   (Well, at the very least a forward travelling hemi-sphere but these details were discussed elsewhere and previously).   Now Huygens principle doesn't say anything about rays, only spherical wavelets BUT you can draw the rays just by noticing that they will always intersect the wavefront at 90 degrees.   So in the diagram above, the spherical wavelet can be considered as rays projected out radially  (that's the blue radial lines).
    So just to be clear:     All along the aperture,   at the left edge of it,  one third of the way along it,  at the centre of it,  four-fifths of the way along it   and  at the far right edge of it...... there are secondary spherical wavelets like this being produced.

   So the earlier diagram  (which I'll repeat below) is NOT really showing one incoming ray reach the aperture and only be deflected "left".   There are rays being sent out from every point along the aperture in ALL directions.    The diagram is just focusing attention on those rays which will converge on a point on the screen labelled   -θ_min,0.    You determine the behaviour at other places on the screen by considering those rays which will converge on that part of the screen.


   If you haven't seen the conventional derivation for the far-field diffraction pattern from a single slit  (sometimes called Fraunhofer Single Slit Diffraction) then I can only apologise and I can understand why your confusion has arisen.   Yes, of course it would seem odd that rays passing through the centre of the aperture are deflected left,  they aren't, there's a spherical secondary wavelet source there and hence rays are being thrown out in ALL directions.   I don't think I have the time to go over the conventional derivation at the moment and the mathematics might be quite dull for most people anyway.   If anyone is interested then ask for it, otherwise that's fine - have a good new year.

Best Wishes.

[alancalverd]

The rectilinear propagation of light derives from the Huygens wavelet model because an infinite number of infinitesimal adjacent wavelets interfere, so the middle of a wide parallel beam  proceeds as a linear wave. Your interpretation prohibits the existence of a parallel beam, but your diagram shows a parallel beam coming from the left, the middle of which suddenly takes it into its mind to diverge. You can't have your cake and eat it!

Fraunhofer diffraction ideally demands a narrow slit where the intensity of diffracted light from both edges is significant compared with the undisturbed primary beam. If that were not so, we wouldn't have geometric shadows or a bright center spot in the pattern you showed. You can eliminate the primary beam with an Arago geometry https://en.wikipedia.org/wiki/Arago_spot which produces a bright center spot caused by interference of the edge diffracted light only, and develop it into an inverse zone plate that adds more intensity to the center spot from more distant diffractive edges.
 

[Eternal Student]

Hi.

Your interpretation prohibits the existence of a parallel beam, but your diagram shows a parallel beam coming from the left, the middle of which suddenly takes it into its mind to diverge. You can't have your cake and eat it!

    That bit is sensible, well done.
    There are, of course, some minor notes:  (i) It's not really my interpretation, it's a mainstream explanation (and I don't know who or how many people developed it).   
    (ii)  The diagram (which also wasn't mine) actually does show a proper (infinite) plane wave approaching from the left if you look carefully.   There are red lines running vertically and  ~  wiggly red lines drawn that intersect those wavefronts at 90 degrees (just like the earlier diagram with radial projected rays) which are effectively treated as light rays.   As you probably know, when the plane wave is infinite then Huygens principle does allow it to progress linearly.
    The full derivation does assume the incident wave was a proper (i.e. infinite width) plane wave.   Exactly as you stated, a wide beam, especially at its centre, is well approximated as a plane wave.   Similarly, if the original light source was a point light source then it does really hit the aperture as a spherical wave BUT this is well approximated as a plane wave (in the region around the equipment) provided the distance from the point source to the aperture is large.

   

Fraunhofer diffraction ideally demands a narrow slit.... (with further comments about beams)....

    The main condition for Fraunhofer (far-field) diffraction mathematics to apply is that   
    with W = maximum distance between two points in the aperture (e.g. its diameter for a round hole);   λ = wavelength of light used;    L = the minimum of length (i) and (ii)  described below:
(i) The distance between the point light source (if the incident wave wasn't genuinely a plane wave but was only approximated as such) and the aperture.     
(ii) The distance between the aperture and the screen.

   So while the easiest way to meet that criteria is to have a small aperture, it is by no means the only way that Fraunhofer diffraction is valid.   Making the distance between the aperture and the screen large compared to the aperture size is also just fine (and is why this thing is often called "far field" diffraction).
    Quick Reference:     https://en.wikipedia.org/wiki/Fraunhofer_diffraction#Derivation_of_Fraunhofer_condition    see especially the condition boxed to the right of that Wikipedia page if you only have 30 seconds to spare.

------
    There is then some mention of a Poission spot (Arago spot was your preferred term).  I'm not sure exactly what that was about.  It sort of blended in with a notion of treating the e-m wave as a set of beams.  You seem to really like a model where you have separate and easily labelled beams.   There's a primary beam and some edge diffracted beams.   I expect you can develop a simple model based on multiple beams with some near the edge of the aperture as the "diffracted beam" but you just don't need to.    There's a perfectly good model for the far field diffraction pattern that doesn't worry itself about "primary beams" and "diffracted beams".  In particular the centre of the incident wave on the aperture (which I think is what you would consider as "the primary beam") is not left alone or assumed to have any special reason to be exempted from Huygens principle.   Everywhere follows that principle. 

Let's take another statement:
   

If that were not so (the slit being narrow?), we wouldn't have geometric shadows or a bright center spot in the pattern you showed.

    You'll always have a geometric shadow because that is just geometry.  I think what you're saying is that it wouldn't always be dark and shadowy in the geometric shadow.   
    The usual single slit diffraction pattern or Fraunhofer diffraction pattern does hold for wide slits, provided the Fraunhofer condition is still met which means the screen is still far away by comparison to the slit width.   The wider the slit, the narrower the pattern on the screen  (e.g the central or 0th order bright region is narrower and correspondingly all other peaks are narrower and also closer -  the whole thing is just squashed in the  "along the screen" axis).  See http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html    for some diagrams.    It is a little counter-intuitive that making the aperture wider actually narrows the central bright region but that's how it is.   The central bright region is never going to be narrower than the aperture because that's only going to happen when the Fraunhofer diffraction condition is no longer met, you can't model everything you need to with plane waves - and at that point a different model for the diffraction must be used.   (There's a Fresnel integral for near field diffraction for example).   
    Another thing which can help to reassure people that the model is still sensible, is that the width of the diffraction pattern is not telling you about the total intensity.  A very narrow aperture does produce a very wide central "bright patch" on the screen but it's not actually bright,  it's just as bright as the pattern is going to get.  In absolute terms it's a very low intensity when the aperture is small and the central bright region will fade below human perception rapidly as you move away from the centre (if indeed you can see anything in the centre at all to start with).  Meanwhile for a larger aperture, even the half-way positions between minima and maxima patches on the screen are still bright enough to be noticed.

    Anyway, if you like an interpretation with "primary beams" and "diffracted beams" then I guess that's fine.   I suppose, it's more intuitive to be thinking that the central part of a beam does just come straight through the centre of aperture unaffected.  Personally, I prefer the Huygens approach - there's nothing special or different about any bit of light anywhere, it all creates secondary spherical wavelets.   (I'm thinking that we might have drifted a long way off the OP,  so I'm just going to stop).

Best Wishes.

[alancalverd]

I spent several happy years making and interpreting x-ray diffraction photographs, every one of which literally had a hole in the middle to let the primary beam out. If we didn't do that, the scattered radiation from the majority of the x-rays that passed straight through the sample would fog the film and make the diffraction spots difficult to find. Hence an abiding interest in knowing the difference.

[hamdani yusuf (OP)]

This diagram may help:



Is there a wavelet propagating from outer circle back to the center?

[hamdani yusuf (OP)]

If you haven't seen the conventional derivation for the far-field diffraction pattern from a single slit  (sometimes called Fraunhofer Single Slit Diffraction) then I can only apologise and I can understand why your confusion has arisen.   Yes, of course it would seem odd that rays passing through the centre of the aperture are deflected left,  they aren't, there's a spherical secondary wavelet source there and hence rays are being thrown out in ALL directions.   I don't think I have the time to go over the conventional derivation at the moment and the mathematics might be quite dull for most people anyway. 

I have seen many of them.

This is from Khan academy, which can be considered a mainstream.

And a follow up video.

If anyone is interested then ask for it, otherwise that's fine - have a good new year.

Since you don't seem to be confused by this experiment result, perhaps you can explain it better than Salman Khan.

Can you derive the interference pattern produced by a thin wire diffraction?

[alancalverd]

I think the answer to "why people confuse them" is because they are badly taught!

Sadly, Khan seems to  be no better than anyone else.

Right from the start, Huygen is a model, not a reason!
The incoming wavefront is curved, as if from a point source. But SSI also occurs with a parallel beam - this is important later on*.
At 3:02 the wavefront in vacuo suddenly terminates at the top. The commentary talks about a barrier but it hasn't reached the barrier yet - no wonder the audience is lost by this stage.
Then he ignores the crucial fact that Huygens requires an infinite number of infinitesimal sources, and constructs a diagram with a finite number of sources that magically take their place as the beam passes through the slit!
*Why did he surmise that, in the absence of diffraction, the central spot would  have a Gaussian intensity distribution? In classical linear optics you would simply get a hard shadow from a parallel beam.

So by 5 minutes into a 15 minute presentation, the audience has already swallowed several red herrings and is rapidly losing its appetite for physics.

[hamdani yusuf (OP)]

I think the answer to "why people confuse them" is because they are badly taught!

Sadly, Khan seems to  be no better than anyone else.

Khan made the video based on textbooks that he read. Based on his resume, he should have read some of the best textbooks available on this issue.

He attended Grace King High School, where, as he recalls, "a few classmates were fresh out of jail and others were bound for top universities."[11] He was a cartoonist for the high school's newspaper.[12] Khan took upper-level mathematics courses at the University of New Orleans while he was in high school and graduated as valedictorian in 1994.[13][14]

He attended the Massachusetts Institute of Technology (MIT), graduating with Bachelor of Science and Master of Science degrees in Course 6 (electrical engineering and computer science), and another bachelor's degree in Course 18 (mathematics), in 1998.[15] In his final year, Khan was the president of the "Senior Gift Committee," a philanthropy program of the graduating class.[16]
https://en.wikipedia.org/wiki/Sal_Khan

This demonstration video from MIT shows what we observe in real life instead of drawing or animation, but unfortunately doesn't even try to offer an explanation.

[hamdani yusuf (OP)]

Here's another video trying to explain single slit diffraction.

Single Slit Diffraction is like getting surprised by a text you just sent yourself | Doc Physics

And here's the channel's description.

https://www.youtube.com/@DocSchuster/about
Description
I am one of four passionate physics teachers at Webster Groves High School in St. Louis, MO.  I teach AP Physics 1 and 2, but I teach calculus with the class as well, since physics makes no sense without it.  I use Walker's excellent textbook, Physics 2nd Edition.  My videos are organized into playlists for each chapter of that book, and really should be watched sequentially if you have the time.

I try to align my class with a first-year physics class at top universities.  You may find the videos useful for tutoring and review.  Please do problems immediately after watching a video.  This is how you will become a stronger physicist.

[hamdani yusuf (OP)]

The incoming wavefront is curved, as if from a point source. But SSI also occurs with a parallel beam - this is important later on*.

A collimating lens or mirror can make a spreading light beam turn into a parallel light beam, which virtually relocate the position of the point source much far away from the slit.

[alancalverd]

Here's another video trying to explain single slit diffraction.

And again, the central ray suddenly diverts to the left for no obvious reason!

[Bored chemist]

A collimating lens or mirror can make a spreading light beam turn into a parallel light beam, which virtually relocate the position of the point source much far away from the slit.

No.
No matter how many times you say that, it still will never be true because of diffraction.

[hamdani yusuf (OP)]

No.
No matter how many times you say that, it still will never be true because of diffraction.

What do you think collimators are for?
Are they all useless due to diffraction?

https://www.britannica.com/technology/collimator
collimator, device for changing the diverging light or other radiation from a point source into a parallel beam. This collimation of the light is required to make specialized measurements in spectroscopy and in geometric and physical optics.

Collimators are optical systems used to imitate standard targets placed in "optical infinity" (very long distance). The collimators are used for projection of image of reference targets into direction of tested imagers.  According to type of optical elements used in design, collimators are divided into two groups: reflective collimators and refractive collimators. Reflective collimators due to their wide spectral range are almost exclusively used in systems for testing thermal imagers and are also preferable in systems testing TV cameras, SWIR imagers, laser systems or multi-sensor surveillance systems. Refractive collimators are mostly used in systems for testing night vision devices or TV cameras working in visible/near infrared range.

From optical designer view, the reflective collimators are inverted telescopes. Therefore it can be claimed that there are many types of reflective collimators depending on mirrors configurations (Newton, Cassegrain, Schwarzschild, Maksutov, etc). However, practically reflective collimators are typically built using Newton design (big parabolic primary, collimating mirror and smaller secondary flat mirror). Next, the reflective collimators can be divided into two basic types:  off axis collimators and on-axis collimators. 

https://www.inframet.com/collimators.htm

[hamdani yusuf (OP)]

Here's another video trying to explain single slit diffraction.

And again, the central ray suddenly diverts to the left for no obvious reason!

Unfortunately, that's what commonly taught in high schools. It would take some considerable efforts to unlearn it and relearn the better explanations.

[Eternal Student]

Hi.

     I only watched bits of the video (and at about double speed) but my opinion was that the video from Khan academy is not perfect.   It's good enough for school level but there are some simplifications that can't really be so easily swept under the rug at University level.   I suppose a 15 minute video is already "long enough" and the presenter probably had their own good reasons for keeping the video short.
     The follow-up video had even more hand-waving or vague argument without much mathematics and I abandoned watching it half way through.  The second half might have been good.

Since you don't seem to be confused by this experiment result, perhaps you can explain it better than Salman Khan.

   Probably not.   I mean let's give the presenter their fair credit here and recognise just how much work would have been required.  At my rate of production it would take hours (days?) to create sufficient text, diagrams and video.   I also probably don't have the right voice or presentation style.   More-over it's sufficiently long and complicated that only someone really interested will watch or read it.   Those wanting a quick impression will just go watch YT videos like that one from Khan academy.

[From Hamdani]    Can you derive the interference pattern produced by a thin wire diffraction?

   Yes, I think so,  although I don't think it's entirely "my" work.   (I'm sure it's in some text books but you would need to get the big ones that specialise in physical optics and not some University textbook that just skims the topic).  Keywords to look up in the index might include "Babinet's principle",  "Aperture function",  "Franhofer integral" and not just "thin wire diffraction".
    Did you really want to see the mathematics?   It's hours (days?) of work to re-create it here on the forum.   Meanwhile there will be one reader and it still only takes a few minutes to ignore it.

 

This demonstration video from MIT shows what we observe in real life instead of drawing or animation, but unfortunately doesn't even try to offer an explanation.

   Yes, that's pretty much what you would get from the mathematics that is being proposed.   That one is a nice video.

Unfortunately, that    (...confusing ideas with rays bending....) is what commonly taught in high schools. It would take some considerable efforts to unlearn it and relearn the better explanations.

    I can basically agree with that.   Schools do not attempt to show the mathematics used and there is inevitably some hand-waving and waffle.   You'd like your pupils to have access to complex numbers, calculus and some appreciation of the wave equation (at least enough to accept that the ODE is linear and sums of solutions are solutions etc.).   It would be much faster if your pupils were already familiar with Fourier Transformations...   So very roughly this is just unlikely to get on a first year University course in Physics,   2nd year+ maybe,  certainly getting it on a school syllabus is really asking too much.

Best Wishes.

[Eternal Student]

Hi.

   I wonder if this is quicker way to convince you that mathematics exists to describe diffraction by a thin wire instead of by a thin slit.

    You (Hamdani) suggested a video by MIT.   They have another video with the same presenter demonstrating diffraction by thin wire.    (Duration about 5 minutes,  available on You Tube,   "Optics: Fraunhofer diffraction - thin wires | MIT Video Demonstrations in Lasers and Optics").

    Now, just spend a moment and ask yourself.... why would the presenter / lecturer have asked the students to calculate the width of the wire(s) if there wasn't some mathematics already available to model this situation? 

   No one is suggesting that Huygens principle is faultless or exactly what is happening at some fundamental level.   However, a few simple assumptions does produce a model which can predict the diffraction patterns you get really well.

Best Wishes.