Why does a light ray BEND when it SLOWS down?

Just curious -

When a light ray changes mediums it speeds up or slows down. It also bends, different colours at different angle. How does it slow down or speed up and bend physically? What happens at the level of atoms and photons to makes this happen?

Bonus Q - When car wheels or fans increase/decrease their speed, we see various spinning shapes moving around at different speeds and directions. Why/how does this happen.

 

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You should do some research on Huygens' Principle, JamesR illustrated its basic consequences for refraction, but there's a lot more detail to it and you can directly derive Snell's law of refraction from it. The explanation actually carries over quite nicely to the wave mechanics found in quantum physics.

That's an optical illusion caused by the human eye's limited refresh rate. Our eyes and brains see moving things much like the frames on a strip of film.

 

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Very concise, clear and simple explanation - nicely done.

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James´ post 2 "answer" does not tell why. It is much like the doctor explaining how sleeping pills work by saying “They contain a narcoleptic agent.” To really tell why, one must explain why light wave (EM waves) shrink their wavelengths more for red than blue when they leave air and go into a transparient medium like glass. Saying that the red bends more, has greater wavelength reduction, is just repeating the observed facts, not explaining them. Why is red light traveling slower than blue light, so has a shorter wavelenth for formation of the Huygen wave fronts at a different angle?

I will only outline the real causal reason why the wave length (c / frequency of the EM wave) makes different changes in the contraction of the wavelength for different EM frequencies:

Transparent materials have very few free electrons. Most >99.9999999999% are bound to an atom. They have a natural oscillation frequency due to the strength of the binding and the mass of the electron, much like a mass hung on a spring does.

When subjected to the Electric Field of the EM wave these electrons are accelerated at the frequency of the driving EM wave. The amplitude of the oscillation depends upon (among other things) on how different the natural bound electron´s frequency is from the EM wave frequency. In general, These natural bound resonances are in the IR. Thus the red light´s lower frequency than the blue light frequency produces greater amplitude oscillation (but not enough to “unbind” the electron*).

Now any accelerated charge produces radiation. The greater the acceleration the stronger the radiation. Thus the EM wave in the transparent material is the sum of two different wave: (1) the driving EM and (2) the secondary wave re-radiated by the accelerated electrons.

I.e. The total wave is of the form Asin(kx-wt) + B sin(kx–wt).

Typically A>> B but the B of red light is larger than the B of blue light. If your recall you trig identities better than I do you will be able to compute C &D in terms of A&B, but the point is that this total wave is of the from Csin(kx –wt +D). where D is the phase shift. I.e. the total wave is of the same frequency as the driven wave but not in phase with it. The D is like a shorting of the null to null gaps (wavelength) and how much dependes upon the frequency of the driving EM waves (how far it is from the natural resonances of the material´s electrons. In other words, the nulls are not moving thru the material as fast. The”phase velocity” is reduced (or increased?) and the “group velocity”.is increased (or reduced?) more for red than for blue light.

It has been more than 30 years since I did these types of calculation and I may have some details wrong, and currently am somewhat confused (which is increased & which is decreased as I do not remember if D is positive or negative) but strength of this interaction between the driving EM wave and the accelerated electron´s re-radiated waves depends upon the frequency of the EM wave. That is why red bends more than blue does.

Once you have a real explanation of WHY there is a differential reduction in the in solid wavelengths, then James´ (really Huygen´s) POV make the bending clear. But it is the wavelength reduction or speed reduction which must be explained. Otherwise one is just re-expressing the facts in other terms, without any explanation of how and why these are the facts. That is OK for doctor´s “contains a narcoleptic agent” hand waving but not for a physicist. We want some details of the mechanism, not a new description in other terms.


*For understanding that one must switch to the photon POV as a finite amount of energy is required “all at once” to free the electron. The blue light (or UV) has this “in solid ionization energy” not the red.

 

Yes if you are not interested in WHY the red light proceeds more slowly than the blue light does in the transparent solid, thus making the red lght´s wavelength shorter than that of the blue.

 

When a car wheel on a video monitor seems to spin slowly forwards or backwards, it is because the refresh rate of the video strobes against the rotation of the wheel. A fan viewed under a fluorescent light gets strobed similarly because of the 60hz power to the fluorescing tube.

 

I find this fascinating Billy, thanks. Is this well established, and does the math bear this out unambiguously? The reason I ask is because I haven't taken an optics course but refraction was explained to me once in a different, less satisfying manner...

 

Warning: Pre-coffee…

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So, why does a photon slow down in a medium?

Yep, you guessed it. The answers for this question...bug me. :grumble:

There are tons of explanations out there. Here is one from ZapperZ at physicsforums, and another from someone at yahoo, who claims to be a quantum physicist.

http://www.physicsforums.com/showpost.php?p=899393&postcount=4

http://answers.yahoo.com/question/index?qid=20090918084206AALZBC5

Well, do you remember that article that I linked about Brian Cox? I also linked it at physicsforums and the author popped in to defend his article. Since he was such a stickler about how physics should be taught, I took the opportunity to ask him this question, as well.

Double Twit Experiment – What Brian Cox Gets Wrong

Perhaps, we should vote on the best answer, eh?

Does anyone know the answer to his last little question?

 

BillyT, as I think about your explanation some more...it raises a couple of questions. I understand that it's been 30 years for you, so if you cannot answer I won't give you too much grief.

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First of all, in your description, the group velocity would not change, correct? Is this borne out by experiment? In other words, is "something" detectable at a distance of ct from a light source regardless of any refractive material between the source and detector? Secondly, while your explanation covers the apparent slowing-down of the phase velocity it doesn't really address the change in direction, does it?

 

As it was explained to me, once, was that refractive material simply absorbs the photons for a bit before emitting them. This idea has some problems but it does make a small amount of sense. Is an atom-bound electron even capable of absorbing any arbitrary photon?

 

Don't they just use the marching soldier analogy to explain this, RJ?

http://www.physicsclassroom.com/class/refrn/u14l1c.cfm

 

Absolutely. It's a nice analogy but it requires a width perpendicular to the direction of travel of the moving object, so it only works with a wave-description (e.g. a small bullet hitting the water at an angle would curve very little, and a point-like photon would not curve at all, which is one of the problems with the explanation I gave). The analogy only holds because the soldiers are trying to stay equidistant from those abreast from them, and I frankly don't know if BillyT's explanation accounts for this.

 

E = hf, where E is energy, h is Planck's constant, and f is frequency

c/wavelength = f, for EMR (. . . f=v/wavelength, in general)

Therefore, as wavelength decreases, at a given v, frequency increases . . . . if frequency increases, the energy E increases.

(IMPO, James)

 

Even though, the EM field perturbs the atom, it is not a true absorption event. So, from what I’ve gathered, we use the phase and group velocities to explain refraction and the Kramers-Kronig relation to understand how the absorption and the refractive index is intertwined. This is characteristic of the many body interaction the electron experiences in the material.

http://en.wikipedia.org/wiki/Kramers–Kronig_relation

http://en.wikipedia.org/wiki/Phase_...ty.2C_refractive_index_and_transmission_speed

I don’t know. I would just like someone to put it all in a nice little paragraph for me. You know, in case one of my shallow girlfriends should ever decide to discuss something other than hair and makeup.

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Trooper #15: "Even though, the EM field perturbs the atom, it is not a true absorption event. So, from what I’ve gathered, we use the phase and group velocities to explain refraction and the Kramers-Kronig relation to understand how the absorption and the refractive index is intertwined. This is characteristic of the many body interaction the electron experiences in the material."

IMPO . . . degree of absorption is dependent upon the relative RI and the nature of the medium (transparent or opaque to EM) . . photon scattering (e.g., xrays) is demonstrable (re: diffraction) which infers some atomic (or at least outer electron) interaction. IMPO diffracton may be a 'special case' of refraction. See my past, related posts elsewhere on Sciforums.

 

The product of group velocity, which I think is the speed of light in the materail, and "phase velocity" is ALWAYS c^2. Thus as the phase velocity speeds up that makes the speed of light slow down.

Yes the slow down of propagation speed is easily detected (now days with pico second duration light and atomic clocks) In fact a few years ago with some materials which do have their natural bound electon frequencies very near that of the light frequency, the speed of travel thru those material can be LESS* than a fast bike rider´s! I think in this case my normal A >> B is revesed to be B >> A.

No James´post 2 does good job of doing that - explaining the bending. My point was that a true "explanation" must mechanistically tell why the light speed in the materail is less and why the reduction is greater for light frequencies closer to the bound electron´s natural frequency of oscillation. For normal transparent materials that is in the IR so red slow more than blue.

* I don´t search much or well (Just use my memory) but bet if you search "slow light" etc you will get a lot of hits. As I recall Physics Today´s cover a few years back had a bike rider beating the light beam in a race.

 

Yes that can help understand why light slows. Newton in fact made basically that argument with his photon POV (he said light was particles and in passing true solids was sort of like soldiers marching thru muddy field had to slow down.)

AFAIK Newton never accept the light is waves, POV of Huygen. Only a mind as great as his could explain the many interference and prism experiments he did with particles. This lead him to get the wavelength dependence of the index of refraction wrong. "Blue soldiers" taking shorter faster steps thru the mud field would be effected MORE than the "red soilders" taking larger, less-frequent, steps.

 

I answered this question here a few months ago. It has to do with the photon inducing shifts in the electron spins and orbits of the atoms in the material it's passing through, and as those shifts occur, the shifting electrons interfere with the probability for the photon to appear at the final destination at a given time. Pretty much it's an extension of the classical electromagnetic explanation which has to do with the electric polarization and magnetic susceptibility of the material.

 

This is probably what I want to know about…but the ole grouch will most likely say, “First, before we waste our time, tell us what you know about quantum electrodynamics.”

Maybe I’ll just reread chapter 3 in Feynman’s QED.


Edit:
^ Opps!

Oh crap, I thought he was snoozing. Sorry, CptBork.

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Do you have the link?