Re: [Phys-L] Why is light slower in glass?

[John Denker <jsd@av8n.com>]

On 01/24/2016 01:04 PM, Savinainen Antti wrote:

> I was asked the question in the title some time ago. 

My answer:  
 a) To a first approximation, the molecules in the glass are 
  little oscillators.  Masses on springs.
 b) To a second approximation, the mass carries an electrical
  charge.  So we have a /charged mass on a spring/.  Roughly
  speaking, the relevant mass and charge belong to some electrons.
  The nuclei are much heavier, so they mostly just sit there.
  They don't contribute to the refractive index.  The electrons
  are attached to the nuclei by springs, i.e. chemical bonds.
 c) The resonant frequency is very high ... higher than ordinary
  optical frequencies.
 d) When light goes through glass, the electric field of the
  light pushes on the electrons.  They move in response ... but
  at optical frequencies they don't move very much, because they
  are being driven off-resonance.  By way of analogy, if you take
  a tuning fork and squeeze the tines together with your hand,
  they will deflect ... but not very much, because you are 
  driving them off-resonance, far below their resonant frequency.
 e) When you drive something at a frequency far below resonance,
  the deflection will be nearly in phase with the force (ignore
  the mass, and you're left with Hooke's law).  This stands in 
  contrast to the far-above-resonance case, where the deflection
  is 180° out of phase with the force (ignore the spring, and 
  you're left with Newton's second law).
 f) The oscillating electrons radiate.  If you work out all the
  phases, including the equation of motion for the electron, and
  the radiation from a moving electron, you find that the new
  contribution to the field is nearly 90° out of phase with the
  incident light, and smaller in magnitude.  If you add this to
  the original incident light, you get a resultant that slightly 
  lags the incident wave.  If you don't believe me, simulate
  it using a spreadsheet.  Add a unit-sized sine plus about
  20% of a cosine and see what you get.
     Hint:  https://www.av8n.com/physics/img48/sine-shift-sine.png
 g) The atoms take "some" energy out of the incident wave, but
  not as much as you might have guessed.  Absorption corresponds
  to the in-phase component of the reradiated field.  It is an
  /even function/ of how far off-resonance you are ... whereas
  the phase shift depends on the out-of-phase component, which
  is an /odd function/ of how far off-resonance you are.  So
  in situations where the refractive index is small, the
  absorption is small squared.  Yet another nifty scaling law!
 h) This is more than you need to know, but this picture is
  consistent with chromatic aberration in lenses.  As the light
  goes up in frequency, the atomic oscillators get closer to
  being on-resonance.  The mechanical response increases, so
  the index increases.

For the next level of detail:
  Feynman volume I chapter 31:  "The Origin of the Refractive Index"
  http://www.feynmanlectures.caltech.edu/I_31.html

Also:
  There should be a way to simulate this in a ripple tank, using
  some lightweight floating objects to simulate the oscillators
  that are excited by the incoming wave and then re-radiate ...
  but I have never tried it and there are a lot of things that
  could go wrong, so this is just a conjecture.  It's not an
  entirely faithful model.  Has anybody done this?

If the student says "waves are OK, but what about photons?" ...
don't take the bait.  Almost everything you need to know about
photons can be explained in terms of wave packets, but not vice
versa; there is no good way to explain waves in terms of photons.

I realize that the essence of critical thinking is to reconcile
each new thing you learn (e.g. waves) with things you've heard
previously (e.g. photons) ... but sometimes this comes down to
realizing that most of what you've been told about photons is
just wrong.  As a matter of engineering, nobody in his right
mind would measure the refractive index using photon counters.
The experiments that actually get done are well described in
terms of waves.

> The student suggested a YouTube video by prof.
> Merrifield: <https://www.youtube.com/watch?v=CiHN0ZWE5bk>
>
> Here is another related video on refraction by prof. Moriarty:
> <https://www.youtube.com/watch?v=YW8KuMtVpug&feature=youtu.be>

In terms of the physics, both of those videos say a lot of things
that are correct, and avoid making any serious technical mistakes.

However, in terms of the pedagogy, it's a disaster.  You should
start by telling students the right answer.  At the introductory
level, students do not need to hear shaggy-dog stories about all
the possible wrong answers.  Later, *after* they have a decent
grasp of the right answer, there will be time to spiral back and
understand what's wrong with each of the wrong ways of looking
at things.

Both of those videos blither at length about a whole bunch of 
irrelevant stuff.  I'm not even going list all the irrelevant
stuff.  It's not even worth explaining why it's irrelevant.




On 01/24/2016 01:47 PM, Shahram Mostarshed replied:

> > Here'sa good explanation by Paul Hewitt:
> >
> > https://www.youtube.com/watch?v=6fSf0lfRLKY

As usual, Hewitt gets the wrong answer.  There are a couple
of ways of understanding why it cannot possibly be correct,
as discussed in the other two videos.