[hamdani yusuf (OP)]

I suppose a 15 minute video is already "long enough" and the presenter probably had their own good reasons for keeping the video short.

He could split it into several short videos. Just make sure that important points are delivered to prevent misunderstandings.

[hamdani yusuf (OP)]

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.

You can finish it anytime you like whenever you are interested in this problem and have the time to spend.

[hamdani yusuf (OP)]

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.

You don't have to create a video. Just mention what's wrong with Khan's videos, and explain what needs to change to make it right.

[hamdani yusuf (OP)]

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.

I've been searching for years. I only found explanations based on Babinet's principle, and then derive the equation based on single slit experiment, assuming that they are really equivalent. I can't find any explanation based on actual geometry of a thin wire.

BTW, I 've made an experiment showing the difference between thin wire and single slit experiment. I'll share it as soon as it becomes available on line.

[hamdani yusuf (OP)]

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.

A few "tweaks" can predict the motion of planets pretty well using geocentric model. They are called epicycles. Just like the explanation on single slit experiment, epicycles also involve changes of movement without physical cause.

[alancalverd]

So here's how it should be taught.

We observe that shadows do not have a true geometric hard edge, so we need something other than a linear ray diagram to describe the phenomenon*.

Huygens proposed a mathematical model in which every point on a wavefront can be considered to be the source of another wave. Note "every". We can then predict the progress of a wave as the integral of an infinity of infinitesimal wavelets.

Consider a tangent to the wavefront. Wavelets orginating from infinitesimally adjacent points will be in phase as the tangent advances, so the net effect of their superposition will be an expanding spherical wavefront from a point source, or a progressive plane wavefront from an infinitely wide parallel beam.

Now consider an infinitely wide parallel beam, interrupted by an edge on the right - a seminfinite front. There being no  sources to the right of the edge, the only contributions downstream come from those "Huygens sources" to the left of the edge, so some of the reinforcing or cancelling wavelets are absent from the downstream wavefront. If we solve the integral at any point downstream it no longer looks like a plane but has ripples caused by the absence of those contributors on the right. We can calculate the distribution of intensity with angle from Huygens' model  if we know the wavelength.

Note that this is an analytic model that gives the observed answer. It does not purport to describe the underlying physics of electromagnetic or any other wave propagation. 

*That's where Khan and all the above diagrams go wrong: they use a finite number of wavelet sources and then have to introduce an absurd ray diagram. You can't mix ray optics with Huygens analysis!

[hamdani yusuf (OP)]

Huygens proposed a mathematical model in which every point on a wavefront can be considered to be the source of another wave. Note "every". We can then predict the progress of a wave as the integral of an infinity of infinitesimal wavelets.

Do you think that Huygen's model is accurate to represent the propagation of light?
Why, or why not?
Does it have any limitations beyond which it's no longer accurate?

[alancalverd]

Do you think that Huygen's model is accurate to represent the propagation of light?
Why, or why not?

Yes, because it does.

As I've shown, it predicts diffraction.

It has a serious limitation because it predicts an equal and opposite backward flow of energy in a parallel beam, which is not observed, so it is a model, not an explanation - you need Maxwell and Poynting to explain unidirectional propagation, and Huygens also becomes less intuitive when the slit is small compared with the wavelength of the light, but strict adherence to it the "infinity if infintesimals" should avoid such nonsense as
 

All the waves passing through the slit interfere to produce a diffraction pattern consisting of bright and dark fringes.

from an internet source that will remain nameless.

[alancalverd]

On further consideration, a proper Huygens analysis avoids the physical nonsense of an edge becoming a source. An edge is a sink, not a source. This is obvious because there is a shadow behind the bulk material, and only one energy source in the system: when we switch off the laser, the edge does not continue to emit light!

The forward wave propagates because each infinitesimal  source of spherical wavelets is surrounded by an infinity of others, so there is only one direction (for a parallel beam - or "any radial direction" for a point source) in which all the secondary wavelets are in phase.

So the wavelets generated near (not "by") the edge are not "surrounded by an infinity of others" and therefore not subject to destructive interference in all but one direction of propagation.

It's still a model but obviously a lot closer to the truth and easier to teach than the drivel in the textbooks. The joy of mathematics is that we can talk about "semi-infinite" wavefronts without embarrassment, and any slit wider than a few microns is two overlapping semi-infinite systems for all practical purposes. It's an odd case of leaping from maths to engineering without passing through any validating physics!

[hamdani yusuf (OP)]

Yes, because it does.

Does it explain diffraction and refraction of light correctly?

As I've shown, it predicts diffraction.

How does it derive equation for diffraction? Can it predict positions of maximum constructive interference?
In the commonly used formula for destructive interference in single slit experiment, why the formula doesn't apply for θ=0?

[hamdani yusuf (OP)]

Here are some effects that happen to a a light beam when it interacts with a macroscopic object (significantly larger than the wavelength).
- It's transmitted. The direction doesn't change.
- It's absorbed. Some of the light energy is converted to some other forms.

- It's reflected. The direction changes, it comes back to the first medium.
- It's refracted. The direction changes, it enters the second medium.
- It's diffracted. The direction changes, it enters the second medium at the edge, and comes out again to the shadow region.

The original light rays and the rays experiencing change of direction due to reflection, refraction, and diffraction can interfere with one another, producing destructive and constructive interference. AFAIK, no one ever mistakenly called interference pattern as reflection pattern nor refraction pattern, even when they are the cause of interfering light rays.

[Bored chemist]

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

Saying it one more time still won't make it true.

[hamdani yusuf (OP)]

Saying it one more time still won't make it true.

What do you think collimators are for?

[hamdani yusuf (OP)]

Yes, because it does.

As I've shown, it predicts diffraction.

How do you explain half interference pattern that I have shown in another thread?

[alancalverd]

Does it explain diffraction and refraction of light correctly?

It models diffraction and refraction well enough that it is used to design lenses. It doesn't purport to explain anything, as I pointed out earlier.

How does it derive equation for diffraction? Can it predict positions of maximum constructive interference?

Yes. It is the basis for all the textbook derivations of diffraction equations.

Your diagram for θ = 0 is incorrect as it doesn't show the effect of a noninfinite beam.

You have made the usual textbook errors of assuming Huygens' infinite array of spherical wavelets  then attempting to represent it with ray propagation of truncated wavefronts.

Beware of being misled by your own models - you could end up like King Canute or even Vladimir Putin!

[alancalverd]

The original light rays and the rays experiencing change of direction due to reflection, refraction, and diffraction can interfere with one another, producing destructive and constructive interference.

Another example of confusing two models. Rays can't interfere - you need waves. We often use rays to model refraction and reflection but they can't model any phenomenon like interference or diffraction.

[hamdani yusuf (OP)]

It models diffraction and refraction well enough that it is used to design lenses. It doesn't purport to explain anything, as I pointed out earlier.

Lenses has been made long before Huygen even lived. They can be designed based on simple ray tracing.

Does it model polarization of light?

[hamdani yusuf (OP)]

The original light rays and the rays experiencing change of direction due to reflection, refraction, and diffraction can interfere with one another, producing destructive and constructive interference.

Another example of confusing two models. Rays can't interfere - you need waves. We often use rays to model refraction and reflection but they can't model any phenomenon like interference or diffraction.

Do you know Lloyd's mirror?

[hamdani yusuf (OP)]

Yes. It is the basis for all the textbook derivations of diffraction equations.

Khan's Academy video shows that it's not the case.

[hamdani yusuf (OP)]

Your diagram for θ = 0 is incorrect as it doesn't show the effect of a noninfinite beam.

What is the correct explanation?
How should the diagram look like?