# Question about refractive index and momentum

I'm probably doing something stupid here...

A wave travels from a medium into a second medium with a smaller refractive index. By definition the speed of the wave increases. Then lambda*f = v, so the wavelength also increases. According to de Broglie, this means the momentum goes down. But how can momentum go down if the wave is moving faster?

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I assume you are talking about like going through glass , Light doesn't slow down in glass or other mediums its just the time lag between absorption and re-emission , in between electrons it is traveling at c . When light goes into glass the frequency doesn't change so
E=hf , E=pc , hf=pc , What you are saying about wave-length may not be applicable in this case ,

That's not entirely correct. The photons actually do slow down. Their frequency remains the same however, and is still useful for calculating momentum. If you want to use wavelength to calculate momentum, you have to use vacuum wavelength.

I assume you are talking about like going through glass , Light doesn't slow down in glass or other mediums its just the time lag between absorption and re-emission , in between electrons it is traveling at c . When light goes into glass the frequency doesn't change so
E=hf , E=pc , hf=pc , What you are saying about wave-length may not be applicable in this case ,
I want to second broean01's observation: the light really does slow down. The siesta description (photon takes breaks) is nowhere near accurate even as a metaphor. Classically, the elecromagnetic disturbance travels slower though the region where the E and B fields feel the overall negative charge; in QM, the photon mixes with some kind of quasiparticle and this mixture has a speed lower than c.

I'm probably doing something stupid here...

A wave travels from a medium into a second medium with a smaller refractive index. By definition the speed of the wave increases. Then lambda*f = v, so the wavelength also increases. According to de Broglie, this means the momentum goes down. But how can momentum go down if the wave is moving faster?
I think the de Broglie relation works "in a vacuum", at least as far as how it maps directly to the wavelength of light. For the quasi-particle mixture thing, you have a non-zero mass so that adds to the momentum too.

That's not entirely correct. The photons actually do slow down. Their frequency remains the same however, and is still useful for calculating momentum. If you want to use wavelength to calculate momentum, you have to use vacuum wavelength.
Light slows down in the denser solid, but its frequency actually increases. This is called conservation of momentum.
The laser at the National Ignition Facility starts out as HeNe red, but thru sucessive passes thru the neodymium-doped quartz, emerges as U/V violet. Energy is gained thru a xenon pump in each quartz block.

Light slows down in the denser solid, but its frequency actually increases. This is called conservation of momentum.
But what about conservation of energy? Doesn't that dictate that the frequency stays constant?

Classically, the elecromagnetic disturbance travels slower though the region where the E and B fields feel the overall negative charge; in QM, the photon mixes with some kind of quasiparticle and this mixture has a speed lower than c.
Interesting , so are you saying that photons are affected by E and B fields , can i alter the photons path with strong E and B fields , What would happen if i did the Stern–Gerlach experiment with photons ,

But what about conservation of energy? Doesn't that dictate that the frequency stays constant?
light has momentum and this momentum is wavelength-dependent (which explains why the photoelectric effect is seen with shorter wavelengths, not greater intensities). THerefore, increase light's momentum by Decreasing its wavelength (becoming more energetic) or increasing its velocity (up to 300KM/sec).
The obverse also holds true: if light's velocity is to slow down (as in the transparent solid), its wavelength MUST decrease (become more energetic). THis is howenergy and momentum are conserved: when the light slows down in the solid, it compensates by increasing its frequency/decreasing its wavelength.

Interesting , so are you saying that photons are affected by E and B fields , can i alter the photons path with strong E and B fields , What would happen if i did the Stern–Gerlach experiment with photons ,
lulz....doing the stern gerlach experiment with photons..lmao i like you guyz......

light has momentum and this momentum is wavelength-dependent (which explains why the photoelectric effect is seen with shorter wavelengths, not greater intensities). THerefore, increase light's momentum by Decreasing its wavelength (becoming more energetic) or increasing its velocity (up to 300KM/sec).
The obverse also holds true: if light's velocity is to slow down (as in the transparent solid), its wavelength MUST decrease (become more energetic). THis is howenergy and momentum are conserved: when the light slows down in the solid, it compensates by increasing its frequency/decreasing its wavelength.
You say that momentum can increase either by increasing speed or decreasing wavelength. If this is the case, then it makes sense that when a photon enters a medium and slows down, its wavelength must decrease to compensate. But where is the equation that governs this? Am I wrong in saying that there is only one expression for momentum of a photon, p=hk? In that case it depends on nothing but the wavelength, but that would mean that conservation of momentum dictates that wavelength is constant, and conservation of energy dictates that frequency is constant, then the velocity should not be able to change at all.

Again, I need an equation here or an explanation of why E=hv or p=hk don't apply. The conceptual arguments aren't going to work unless you make a much clearer distinction between energy and momentum (or wavelength and frequency) than you made in the last post.

I feel like there has to be a simple explanation for the confusion here, but I haven't seen it yet!

I think the de Broglie relation works "in a vacuum", at least as far as how it maps directly to the wavelength of light. For the quasi-particle mixture thing, you have a non-zero mass so that adds to the momentum too.
Are you saying that, in some sense, photons have a mass when they travel inside a medium?

Interesting , so are you saying that photons are affected by E and B fields , can i alter the photons path with strong E and B fields , What would happen if i did the Stern–Gerlach experiment with photons ,
No, I said that classically an elecromagnetic wave is the E and B fields. This is still useful for radio. Their mutual propagation is affected by passing through matter which is full of bound electrons. This is plugged in as the http://en.wikipedia.org/wiki/Permitivity" [Broken] of the space.

Switching to the quantum model, E and B fields do not affect photons, as photons are not charged.

And yet, radio waves will make the unbound electrons in a long conductor slosh back and forth, since they are E and B fields. Explaining that using the quantum model uses the concept of "Polariton"[/URL] quasi-particles.

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Are you saying that, in some sense, photons have a mass when they travel inside a medium?
"In some sense," yes. In fact, in precisely this way.

Again, I need an equation here or an explanation of why E=hv or p=hk don't apply. The conceptual arguments aren't going to work unless you make a much clearer distinction between energy and momentum (or wavelength and frequency) than you made in the last post.

I feel like there has to be a simple explanation for the confusion here, but I haven't seen it yet!
Because you are not dealing with photons. You are dealing with polaritons, which are a quantum mixture of photons and quantized electron density waves in the material.

Claude Bile
Frequency (and thus energy) does not change when moving from one medium to another. This constraint is required to preserve continuity of E and B fields across an interface between media of different refractive indices.

Claude.

"In some sense," yes. In fact, in precisely this way.
Well in some sense mass is just the extent to which a particle doesn't behave like those that travel at the speed of light. The fact that photons are massless does not prevent them from exerting a gravitational influence, for instance. If photons didn't have a gravitational influence, momentum would not be conserved during gravitational redshift.

the light really does slow down.
so when the light does get back back up to c can we calculate the acceleration .