Refraction of Light: Myth or Reality?

[sophiecentaur]

a paraxial ray, which should be able to carry on in a straight line seeing no change in index, always is aware of the different indices on either side and curves into the denser material.

We just had a thread about 'how do the electrons know where to go?" and the opinion was that anthropomorphism has no place in Physics. The same thing applies here. If a small deviation left or right will cause a 'restoring' motion then where is the problem? The deviation can be a small as you like and there will always be deviations due to thermal effects.
Fermat's Principle should operate even when there is an apparent plateau involved. That graded index fibre certainly is a smart idea. Just imagine some guy waking up in the middle of the night with the idea and wondering if it would work. Too good to be true!

 

[hutchphd]

I know exactly what your teacher is trying to describe. And your teacher's explanation is rubbish. He is using the marching soldiers or the two wheels hitting the sand analogy you see here.

Is Huygens Principle rubbish?

 

[Jaffer2020]

Just before this thread ends, can I ask about a couple of points which puzzled me?

No one commented on this, but I didn't understand where the electrons came from in a vacuum?

Oops, sorry that was a mistake on my end, I meant in a medium, not a vacuum.

 

[Jaffer2020]

Note that this is a pretty much simplified picture too, even within this classical approach, and it's valid only when $\omega$ is not too close to an eigenfrequency of the harmonically bound charges, $\omega_0$. If if $\omega$ comes close to such an eigenfrequency, you have "anomalous dispersion", where you need a more refined treatment of this model.

Is the eigenfrequency just another term for the natural/resonant frequencies of some system, or is it different?

 

[Hal Jordan]

I have found that the best thing to do with students at this level is to show them demonstrations of refraction, picque their interest and discuss the simplest “theories” for why this occurs. The interested ones will then go from there on their own, the others well...they will do what they always do. We have to remember that no matter how elaborate or at what level taught, these are all theories - we do not “know.”

Every generation thinks they have a lock on knowledge only to be upstaged by the next. Ensure you present material as, “This is what we believe causes this to happen.” Maybe they will be challenged to look harder for the answer.

 

[vanhees71]

Is the eigenfrequency just another term for the natural/resonant frequencies of some system, or is it different?

Yes, it's the resonant frequencies of the system.

 

[sophiecentaur]

Is Huygens Principle rubbish?

Has anyone suggested that it is? I can't see that the teacher was presenting any form of Huygens. There are a number of analogies to show how a wave front can change direction but they do not involve a 'reason' for change of wave speed - and neither does Huygens. In fact there are many theories from the past which are described, these days, in terms of what has been found out subsequently.

 

[hutchphd]

The term "rubbish" was applied to the wheel and axle explanation of the result of Huygens on the wave front. The speed change was a given at that point. It seemed to me a clever explanation but apparently was not admired by @Dr_Nate; I was questioninq both his analysis and his use of the word.

 

[vanhees71]

For the wave equation in 3 (spatial) dimensions the Huygens principle is correct. It's known as the regarded Green's function.

 

[sophiecentaur]

For the wave equation in 3 (spatial) dimensions the Huygens principle is trtcorrect. It's known as the regarded Green's function.

I have to ask you at what age were you introduced to Green’s function and the maths of a wave function. How you would have dealt with it in tenth grade.
it’s a real potential failing of PF that contributions to virtually any thread are subjected to intellectual inflation and the ball is so often stolen from the OP.
How to present hard concepts at all levels is a very valid talking point. Perhaps the levels of posts should be policed stronger and the meaning of “off topic” could be re-examined.

 

[hutchphd]

This has come back from from an unexpected direction. I agree with both preceeding comments.
I thought the characterization of the teachers attempt to simplify the explanation (in a perfectly Huygens-reasonable way) as rubbish was unwarranted. Similarly Huygens is conceptually not that difficult and really is just a statement about the retarded Green's function.
My original complaint was I fact about my perception of intellectual snobbery (or snub-ery)

 

[sophiecentaur]

My original complaint was I fact about my perception of intellectual snobbery (or snub-ery)

Oh yes, there is plenty of that about but there is another aspect of 'telling people about things' and that is age appropriateness. There would be no point in trying to explain a phenomenon to a five year old in terms of maths or even 'Science reasoning'. It's not being snobbish to limit ones reaction to a young child's question to 1. Confirming that what they saw is what we all see and 2. Describing similar examples in other contexts, perhaps giving it a name for future reference.
Story: I was walking down our back lane with my little granddaughter (hah - those were the days!) in the late afternoon and the Sun was low in the sky, the other side of a sparse hedge. She excitedly remarked that the Sun was following us. Should I have told her about the geometry of parallax? That would have brought the shutter down for another couple of years. I simply pointed out that distant trees were doing the same thing and that it was all to do with distance and waved my arms about a bit. In her case, there is another factor. She has rather serious strabismus and it is doubtful whether introducing binocular vision would have helped - so I didn't. Did she miss out in any way, from my reaction?