Refraction of Light: Myth or Reality?

[Jaffer2020]

In my latest 10th grade physics lesson, we were learning about the refraction of light. I decided to share what I knew about why light slows down in a vacuum, which is, in short, because the electric field of the electromagnetic wave exerts a force on the charged electrons of a medium, which in turn causes the electrons to oscillate and create their own electric field wave, creating a new slower net superimposed wave.

As for the bending of light, it is due to the increased permittivity constant of the medium, which affects the components of the electric field and changes its direction.

However, at school, the teacher said that my first explanation was rubbish and that light slows down because the medium is denser and light 'has a harder time moving'. For the bending of light, he depicted it as an object moving from sand to mud, which slows it down on one end of the object, which changes the direction of the light.

From what I have heard, these are erroneous descriptions of refraction, but it is what we are taught. Are these temporary descriptions of refraction, or is it what we're going to stick to forever ?

 

[hutchphd]

Of course the actual description of light requires quantum field theory so the term "actual" is a relative thing when you ask why.

1. I do not see that your description and your teachers are at odds for the speed issue: both are sort of correct
2. please explain in detail how your explanation causes "bending"...I would give the prize to your teacher on this one.

And now I get to quote my favorite Feynman answer about "why" questions:

 

[Jaffer2020]

@hutchphd, thank you for the clarification. Perhaps "why" isn't the best way to phrase the question. As for the bending of light, I tried to explain it in the image below (I hope it's clear enough to read). This is, from what I've learnt, out of the school curriculum , the classical approach to refraction, although there are other explanations (e.g QFT, principle of least action etc.).

 

[DaveE]

I think these 2 videos are the best description I know of. Frankly, this is way beyond 10th grade physics if you keep digging deeper.

 

[sophiecentaur]

However, at school, the teacher said that my first explanation was rubbish and that light slows down because the medium is denser and light 'has a harder time moving'

Your initial attempt at an explanation was not as good as it could have been because you were concentrating on (and over simplifying) the properties of the media and trying to explain them, rather than going for the main principle involved - which is time taken.
'a harder time moving' really doesn't fit in any explanation at any level so your teacher let you down, I think. There is a perfectly reasonable level of explanation, based on the speed of the light in various media - without muddying the water with an over simplification. If you accept that wave speed varies according to the properties of the medium (not just "density", which is far too simplistic) then you can show that Snell's Law describes the path that involves the shortest transit time. (Fermat's Principle etc.) Any other path would involve the light taking longer to get there. The same geometry applies to a man running and swimming to a point on the other side of a swimming pool. The quickest path is found by that same Snell's Law calculation, using his swimming and running speeds.

 

[Jaffer2020]

If you accept that wave speed varies according to the properties of the medium (not just "density", which is far too simplistic) then you can show that Snell's Law describes the path that involves the shortest transit time. (Fermat's Principle etc.) Any other path would involve the light taking longer to get there. The same geometry applies to a man running and swimming to a point on the other side of a swimming pool. The quickest path is found by that same Snell's Law calculation, using his swimming and running speeds.

It also depends on the material itself, the molecular structure and so on, right? The way the teacher explained it to the class was using the idea of the photons behaving as particles, acting in the classical sense. If I put myself in the shoes of the other students, this idea would make me think of the light moving with some mass, whose motion is being resisted by the material, which from what I know is not the case. I get that my explanation was not complete, but the simplified idea that the photons exert a force on the electron, which oscillate, forming another wave, interfering with the light wave and creating a final wave of a slower velocity, sounded like a more complete explanation than 'the density of the material slows light down'.

Also, the Fermat principle is just another way of explaining the principle of least action/time, correct ? (Calculated by using the Feynman path integral, which finds the fastest route from point A to point B, like how in classical mechanics the Lagrangian and action are used ). In this case, the path is one which takes the shortest time in total, including the difference in velocity of the media, which is given by Snell's Law: n1θ1 = n2θ2, where n is the refractive index of the media and theta is the angle from the normal. Am I correct in saying this ?

 

[Jaffer2020]

I think these 2 videos are the best description I know of. Frankly, this is way beyond 10th grade physics if you keep digging deeper.

I have watched, Professor Merrifield's (top video) on this matter and I think he had a very elegant explanation. I tried to use a similar but shorter explanation in class, but the teacher dismissed it. I don't know if it's because the curriculum tries to keep it simpler than this, in order to not confuse the majority of 10th graders or if it's not a widely accepted idea. Like Prof. Merrifield says, there are many misconceptions of the idea.

 

[hutchphd]

As for the bending of light, I tried to explain it in the image below (I hope it's clear enough to read). This is, from what I've learnt, out of the school curriculum , the classical approach to refraction, although there are other explanations (e.g QFT, principle of least action etc.).

I applaud greatly your attempt to understand behavior of the E field at the surface, but your attempt is incorrect in ways that you will learn...frankly more than I can cover here. Really the subject of college level course (as Griffiths book)
Perhaps the most telling indication is that refraction happens for any kind of wave (sound, ocean, or electromagnetic; tranverse or longitudinal) at a plane interface where the speed changes. So worrying about the E field is not the easiest path to understanding, because light is quite complicated.
A simpler correct explanation for refraction of waves comes from either Huygens construction or (from a different perspective) Fermat's principle as discussed by other learned folks here and yourself.
The issue of speed of light in media is as complicated as you wish to go into. But you do need to really know the basics first. Learn what you can from those around you.

 

[Jaffer2020]

I applaud greatly your attempt to understand behaviour of the E field at the surface, but your attempt is incorrect in ways that you will learn...frankly more than I can cover here. Really the subject of college level course (as Griffiths book)

Are you able to briefly explain where I went wrong? So that I can keep a note of it. I started to read Griffith's "Introduction to Electrodynamics" book and Daniel Fleisch's "Student's Guide to Maxwell's Equations" and have so far only read up to Gauss's Laws:
∇⋅E = ρ/ε (For Electric Fields)
∇⋅B = 0 (For Magnetic Fields)
I am really interested in the topic and would like to learn it in depth (I am comfortable with Calculus and Linear Algebra), so I enjoy perfecting the details, to ensure I don't make mistakes.

 

[hutchphd]

Well, to start with, light is inherently an electrodynamic (i. e. not electrostatic) phenomenon so you need the full power of Maxwell's equations (which are extensions of Gauss and Faraday) and their extension into linear media. The constants you used also are frequency dependent (you used the static values). Then you need to understand fundamentally how the wave equation is contained in the Maxwell Equations for free space. Once you know this you will know a lot! It will take some time and cogitation. Work the problems. Learn deeply.
I like Griffiths very much. I like Feynman's Lectures. I don't know Fleisch but it sounds like a good idea. And your teacher may be more use than you think!

 

[DaveE]

your teacher may be more use than you think!

Yes. You are dealing with a subject that is way more complicated than any 10th grade student or teacher can fully comprehend. At this level there aren't really correct answers, just good analogies, which are all wrong, of course. So you are right to be skeptical. Many explanations are fundamentally wrong. You may be better off just saying I don't know, than buying into some story about light hitting atoms, etc.

I wouldn't worry about it at this stage, just accept that light travels more slowly in dense materials. Once you really know calculus and Maxwell's equations you can get further along. When you are good at quantum mechanics, then maybe you'll really understand this stuff.

I would wager that most of the people here, like me, have had productive careers in the physical sciences without understanding this stuff 100%. I recall the old physics joke, that every physics class starts off by telling you that what we taught you last year was wrong.

 

[Jaffer2020]

Once you really know calculus and Maxwell's equations you can get further along. When you are good at quantum mechanics, then maybe you'll really understand this stuff.

I'm reading Leonard Susskind's "Quantum Mechanics Theoretical minimum", Feynman's "QED", Griffith's "Intro to electrodynamics" and Daniel Fleisch's "Student's Guide to Maxwell's Equations". What other resources do you recommend for electrodynamics and Quantum Mechanics? Ones which don't rely solely on analogies and popular explanations but instead in the Math and real science behind it all. Thank you.

 

[sophiecentaur]

The way the teacher explained it to the class was using the idea of the photons behaving as particles, acting in the classical sense. If I put myself in the shoes of the other students, this idea would make me think of the light moving with some mass, whose motion is being resisted by the material, which from what I know is not the case. I get that my explanation was not complete, but the simplified idea that the photons exert a force on the electron, which oscillate, forming another wave, interfering with the light wave and creating a final wave of a slower velocity, sounded like a more complete explanation than 'the density of the material slows light down'.

I tried to use a similar but shorter explanation in class, but the teacher dismissed it

The title of the thread implies that a Tenth Grade explanation of the phenomenon is appropriate. I live in the UK but my understanding is that the age group is around 14 / 15 years. If that's the case then the majority of your class will not have been taught detailed EM theory or of Quantum Theory or any Solid State Physics. Attempts to describe the interaction of EM waves and matter, based on classical 'little bullet' descriptions of photons will be full of holes. Whatever you heard in a tenth grade lesson is unlikely to be at a level with much that is being discussed in this thread. You appear to have read around much more than normal for a student at your grade so you will find several annoying clashes with your National Curriculum (and your teachers' interpretations it). You may be lucky and your teachers may be more knowledgeable than required at that level of teaching but their main job is to get you through appropriate exams. Boring for you, perhaps but a real life situation.

 

[PeroK]

I'm reading Leonard Susskind's "Quantum Mechanics Theoretical minimum", Feynman's "QED", Griffith's "Intro to electrodynamics" and Daniel Fleisch's "Student's Guide to Maxwell's Equations". What other resources do you recommend for electrodynamics and Quantum Mechanics? Ones which don't rely solely on analogies and popular explanations but instead in the Math and real science behind it all. Thank you.

First, you need to understand (as I think you do) that there are two main theoretical models for light: classical EM, as covered in Griffiths; and, QED, as described by Feynman.

The classical theory of refraction is covered in Griffiths, section 9.3.3. Essentially, the light refracts in order to satisfy Maxwell's equations in two media with different refractive index.

You could try to explain this further in terms of bringing in why the refractive index of glass is different from air, say. This is covered by Griffiths in section 4.4.

The QED model is clearly very different, although it must predict the same phenomenon. That's covered in chapter 2 of Feyman's book. Can you make sense of Feynman's book? I think it's great, but I'm not sure how anyone could really understand what he's saying without some knowledge of QM and probability amplitudes.

 

[sophiecentaur]

First, you need to understand (as I think you do) that there are two main theoretical models for light: classical EM, as covered in Griffiths; and, QED, as described by Feynman.

The classical theory of refraction is covered in Griffiths, section 9.3.3. Essentially, the light refracts in order to satisfy Maxwell's equations in two media with different refractive index.

You could try to explain this further in terms of bringing in why the refractive index of glass is different from air, say. This is covered by Griffiths in section 4.4.

The QED model is clearly very different, although it must predict the same phenomenon. That's covered in chapter 2 of Feyman's book. Can you make sense of Feynman's book? I think it's great, but I'm not sure how anyone could really understand what he's saying without some knowledge of QM and probability amplitudes.

This, and several other of the posts on this thread are good reading and informative but could you tell me what they have to do with Tenth Grade Physics? The OP made a point of saying that he wants a tenth grade explanation so why not address that? Can anyone tell me where QED shows up in Tenth Grade?

 

[PeroK]

This, and several other of the posts on this thread are good reading and informative but could you tell me what they have to do with Tenth Grade Physics? The OP made a point of saying that he wants a tenth grade explanation so why not address that? Can anyone tell me where QED shows up in Tenth Grade?

He also said:

I'm reading Leonard Susskind's "Quantum Mechanics Theoretical minimum", Feynman's "QED", Griffith's "Intro to electrodynamics" and Daniel Fleisch's "Student's Guide to Maxwell's Equations".

Hence my references to these books.

Given this the title could be changed and the level upgraded to intermediate.

 

[sophiecentaur]

@PeroK I agree with you, of course and my main criticism is of how the teacher attempted to present the subject (and failed) in a strange combination of intuition and a hundred+ year old model of photons.
The OP is clearly working way out of the curriculum. Unless the class is very non-typical, most of them must spend a lot of lesson time in a pretty confused state if the teacher spends time addressing the OP’s contributions.

 

[hutchphd]

This, and several other of the posts on this thread are good reading and informative but could you tell me what they have to do with Tenth Grade Physics? The OP made a point of saying that he wants a tenth grade explanation so why not address that? Can anyone tell me where QED shows up in Tenth Grade?

I believe I did exactly that by suggesting either Huygens or Fermat.They can be easily constructed using a compass and ruler. Without handwaving.
Then I supplied Feynman's inimitable "why" answer to tell him there are always deeper layers..
So please supply your tenth grade explanation for the speed of light in matter... I still say neither he nor his teacher were completely wrong...

 

[hutchphd]

Summary:: Is the description of the refraction of light in 10th grade a simplified version of the real reason or is it just misinformation?

As for the bending of light, it is due to the increased permittivity constant of the medium, which affects the components of the electric field and changes its direction.

This is as simple as I will go ...it is not simple:

https://www.feynmanlectures.caltech.edu/I_31.html.

 

[epenguin]

Also, the Fermat principle is just another way of explaining the principle of least action/time, correct ? (Calculated by using the Feynman path integral, which finds the fastest route from point A to point B, like how in classical mechanics the Lagrangian and action are used ). In this case, the path is one which takes the shortest time in total, including the difference in velocity of the media, which is given by Snell's Law: n1θ1 = n2θ2, where n is the refractive index of the media and theta is the angle from the normal. Am I correct in saying this ?

Maybe in a complete wave theory, but if you are talking about paths in this way, thinking of straight line paths aka "rays" Fermat's principle works OK - except you need to light to be traveling faster in glass than in air for example. Which it could have done as far as Newton or Fermat knew. If instead you want it to be slower in glass maybe it works as longest time (compared to neighbouring straight line paths).(?)

 

[hutchphd]

Maybe in a complete wave theory, but if you are talking about paths in this way, thinking of straight line paths aka "rays" Fermat's principle works OK - except you need to light to be traveling faster in glass than in air for example. Which it could have done as far as Newton or Fermat knew. If instead you want it to be slower in glass maybe it works as longest time (compared to neighbouring straight line paths).(?)

This is not correct. Please see

https://en.wikipedia.org/wiki/Snell's_law#Derivation_from_Fermat's_principle

 

[Jaffer2020]

Can you make sense of Feynman's book? I think it's great, but I'm not sure how anyone could really understand what he's saying without some knowledge of QM and probability amplitudes.

I can't summarise everything I know about QM or QFT on this thread, but as for the probability amplitude, I can share what I have learnt. From what I know, the probability amplitude is the coefficient of some possible state, which when squared, gives you the probability of that state happening. So in Dirac Notation:

|A> = a vector space
(a₁,a₂,a₃...a_n) = components of |A>
|A> = a_x|x >+a_y|y>
where a_x and a_y are the probability amplitudes of states |x> and |y> respectively.
The probability of, say, |x> would be = a_x*a_x = <A|x><x|A>
where a_x* is the complex conjugate of a_x​

This was not covered in my 10th grade class, I just happened to be interested in the topic.

​

 

[PeroK]

I can't summarise everything I know about QM or QFT on this thread, but as for the probability amplitude, I can share what I have learnt. From what I know, the probability amplitude is the coefficient of some possible state, which when squared, gives you the probability of that state happening. So in Dirac Notation:

|A> = a vector space
(a₁,a₂,a₃...a_n) = components of |A>
|A> = a_x|x >+a_y|y>
where a_x and a_y are the probability amplitudes of states |x> and |y> respectively.
The probability of, say, |x> would be = a_x*a_x = <A|x><x|A>
where a_x* is the complex conjugate of a_x​

This was not covered in my 10th grade class, I just happened to be interested in the topic.

​

You're a long way ahead of the game, in any case!

 

[etotheipi]

Can anyone tell me where QED shows up in Tenth Grade?

I think it's just before the module on superstring theory.

 

[Jaffer2020]

I think it's just before the module on superstring theory.

That might be 9th grade actually.

 

[Dr_Nate]

For the bending of light, he depicted it as an object moving from sand to mud, which slows it down on one end of the object, which changes the direction of the light.

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.

 

[vanhees71]

First of all, to understand macroscopic electrodynamics in media quite well you don't need QFT right away, except you want a first-principle description of the medium in terms of quantum-many-body theory.

Qualitatively you can describe a dielectric body (i.e., a non-conducting material) as a set of bound charges, which are at rest (mechanical equilibrium) when no external electromagnetic field is present. If now an em. wave with fields not too strong interacts with these charges in the body, they are somewhat displaced from their equilibrium placed, and the reaction can be described as a damped harmonic oscillator force. Thus, the charges start to oscillate around their equilibrium places and since they are thus accelerated they emit electromagnetic waves themselves. After some "relaxation time" the motion of the charges is such that they oscillate with the same frequency as the incoming wave, and the electromagnetic field in the medium itself becomes also such a wave. The difference to propagation in free space then boils down to a change in the electric permittivity, which depends on the frequency of the incoming wave, i.e., instead of $\epsilon_0$ in the vacuum you have $\epsilon(\omega)=\epsilon_r(\omega) \epsilon_0$. Neglecting magnetic effects the permeability stays the same as in the vacuum, $\mu_0$. This means the phase speed of light changes from $c_0=1/\sqrt{\mu_0 \epsilon_0}$ to $c=1/\sqrt{\mu_0 \epsilon}=c_0/n$, where $n=\sqrt{\epsilon_r}$ is the index of refraction of the medium. If $\omega$ is in a region of "normal dispersion", usually you have $\epsilon_r>1$ and thus $c=c_0/n<c_0$.

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.

 

[sophiecentaur]

So please supply your tenth grade explanation for the speed of light in matter...

There is no tenth grade explanation. If you want a suitable explanation for the OP then it is a totally different matter. Teaching schemes are invented to impress 'our masters' and they earn brownie points by asserting that students 'get things' - often with very little evidence. The way to present it to tenth grade is that some media let light through them. The speed through all media is less than it is in a vacuum. There is a general principle that the speed is related to density but not in a simple way. The wavelength diagram leads convincingly to Snell's Law. (Photons are useless for most explanations) The very fact that teachers try the marching soldiers model merely demonstrates my point. Most Tenth grade students want facts and basic rules; something to hang onto when new stuff comes along.
People (bright PF members, in particular) tend to forget just how most 14 year old kids think. They mostly don't operate at the Formal Operational level. (See the Piagetian levels of cognitive development and remember that Piaget dealt with the well educated children of his professional Swiss friends; he incredibly overestimated kids in general.) Most adults are only scraping the Formal Operational for all their lives. Why do you think there are endless conversations about football scores and players in pubs? Such conversations are full of facts and assertions with no actual 'arguments' involved. No Formal Operational there at all and no insult is intended in my comments. If I pointed out that most people cannot run a Marathon or hear 22kHz, no one would be offended.

 

[Merlin3189]

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

... I knew about why light slows down in a vacuum, which is, in short, because the electric field of the electromagnetic wave exerts a force on the charged electrons of a medium,

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

In post #3, I couldn't follow the logic here about parallel and perpendicular components of E field. Particularly as I'd expect the wave to slow down for normal as well as oblique incidence.
The point about E fields perpendicular and parallel to the orientation of the crystal lattice seems vaguely familiar for birefringent materials, but I don't understand it for isotropic materials.

No big deals. If they're just random obiter dicta of no consequence, I shall lose no sleep. Just wondering if there are holes in my knowledge, even at grade 10 !

My own position is that, afaik I only encounter phenomena that require light to slow down in some media, and I believe it does as an experimental fact. I sometimes wonder exactly how this comes about, but don't feel any great need to know that, as it doesn't come up as a bar to understanding most phenomena I've thought about.

I suppose the most worrying for me, is the variation with frequency (dispersion?) If I knew why it slowed down, I might understand why the degree depended on frequency. Having watched those 60 Symbols videos again, I doubt that I ever shall though!

Less worrying, but more intriguing perhaps, is why in graded index fibres/lenses 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. Always seems cart before the horse that it changes speed after it has decided to change direction.

 

[vanhees71]

If you want to understand refraction in detail you have to solve the Maxwell equations using the appropriate boundary conditions at the surface of the medium. There you have to disinguish between polarizations in and perpendicular to the plane of incidence. The result are the Fresnel equations:

https://en.wikipedia.org/wiki/Fresnel_equations

Of course, if you have anisotropic media (crystals) you have a tensor of electric susceptibility and the issue becomes more complicated:

https://en.wikipedia.org/wiki/Crystal_optics#Anisotropic_media

 

[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.