Light Through a Medium: Exploring the Physics

[M Grandin]

Huygens Principle

This leads to interesting thoughts about "Huygens Principle", according to for instance site

http://www.mathpages.com/home/kmath242/kmath242.htm

As hinted there, also traveling matter may be regarded as fluctuating waves between -C and + C velocities, where resulting "group velocity" is the observed velocity. Appear fruitful trying generalize Huygens principle, that could perhaps also explain "Einstein relativity" in a more common-sense way.

 

[Claude Bile]

I know what you mean about how the phase difference will be cumulative, and how it will slow down, however I do not see where this "phase difference" comes from...I do not believe you have elaborated on this so far...I would much appreciate if you could explain this phase difference in some physical manner.

The phase difference is a standard property of any driven oscillator. If you drive an oscillator with a resonance at frequency $\omega_0$ at some non-resonant frequency $\omega$, then the driving force will not be in phase with the motion of the oscillator.

The converse case, where the driving force IS in phase with the motion of the oscillator is the very definition of a resonance, since the driving force is ALWAYS in the same direction as the oscillator motion, hence energy is coupled into the oscillator very efficiently. Since we are not at resonance in the case of transmission, there must be some phase difference between the driving force (i.e. the incident E field) and the motion of the oscillator (i.e the response field).

Claude.

 

[kcodon]

Thanks Claude.

I haven't been able to reply as soon as I would have liked, however I'd like to thank you for your perseverance! I finally found a site that explained the phase difference you keep referring to, and I think I now see how this applies to the transmission of light. Its gloriously more simple than things I was imagining, so thanks again,

Kcodon

 

[GT1]

Thanks Claude.

I finally found a site that explained the phase difference you keep referring to, and I think I now see how this applies to the transmission of light. Its gloriously more simple than things I was imagining, so thanks again,

Kcodon

Can you please add the link?

 

[kcodon]

The phase difference is a standard property of any driven oscillator. If you drive an oscillator with a resonance at frequency $\omega_0$ at some non-resonant frequency $\omega$, then the driving force will not be in phase with the motion of the oscillator.

The converse case, where the driving force IS in phase with the motion of the oscillator is the very definition of a resonance, since the driving force is ALWAYS in the same direction as the oscillator motion, hence energy is coupled into the oscillator very efficiently. Since we are not at resonance in the case of transmission, there must be some phase difference between the driving force (i.e. the incident E field) and the motion of the oscillator (i.e the response field).

Claude.

Hi GT1,

Claude puts it nicely, but this site http://perlnet.umaine.edu/IMT/FHM/IG%20FHM.pdf"
helped me understand a bit more. I doubt you will find it useful, as it's actually like a lesson plan and not exactly an orthodox explanation, however see for yourself.

I never understood how two dipoles could have this phase difference. However basic idea - at least I think - is that the dipole A drives dipole B when dipole B is at max velocity, opposed to at max displacement, if that makes sense. Think of a swing...one would intuitively expect that the dipole would be similar to the swing case...providing the driving force (pushing swing) at max displacement (when swing at peak), however I don't think this is the case...the drive is provided not at the peak. This is the phase difference. How this slows down light transmission: think of a line of swings. If each one doesn't drive the other at the "peak", then can you imagine how that slows it down?

Another site to see the effect of this phase difference is http://webphysics.davidson.edu/faculty/thg/physlets/html/driven_sho.html"
Hope it helps,

Kcodon

 

[Claude Bile]

Thanks Claude.

I haven't been able to reply as soon as I would have liked, however I'd like to thank you for your perseverance! I finally found a site that explained the phase difference you keep referring to, and I think I now see how this applies to the transmission of light. Its gloriously more simple than things I was imagining, so thanks again,

Kcodon

No problem, glad to see I was a help rather than a hindrance .

Claude.

 

[GT1]

Thanks Kcodon!

 

[catkin]

Why does light propagate slower in a medium than in a vacuum? As a perturbed atom passes the pertubation on to the nest atom, there is a slight shift in the phase of the oscillation of the two atoms. The culmination of these phase shifts manifests itself as a reduced velocity.

Thanks for that; it's the closest I've found to a satisfying explanation but I'm still curious.

How wrong is the following wild theorising? The photon is a probability density wave function, not actually manifested at any place along that wave function until it interacts with another probability density wave function when both probability density wave functions have to collapse. In the case of light (photon) transmission through a medium, the photon's wave continues to move at the speed of light but the centre of probability density (the place the photon is most likely to manifest if it must) slides backwards along the wave. The only way we can measure the photon is by making it manifest thus all our observations relate to the the centre of probability density and so indicate that the photon is traveling slower in the medium than in a vacuum.

I'm particularly worried by "The only way we can measure the photon is by making it manifest"; what about all the experiments that demonstrate wave-like properties? And by the implicit assertion that the centre of probability density is made to slide backwards without any interaction that would require collapse of the wave function.