Why Does Light Travel at Different Speeds in Various Media?

[pivoxa15]

The velocity of different frequency light in a fixed medium is different. In other words the index of refraction of different light in a given medium is different. This fact could explain chromatic dispersion. But why? What physics can explain this phenomena?

I realize that in the vaccum, all light travel at a fixed speed. So the difference in speeds in a material must be because of the material and not an intrinsic property of light. I notice that light of higher frequency has a higher index of refraction compared to lower frequency light. This could be due to higher frequency light more frequently colliding with the atoms in the material hence appear to pass the material slower. Thereby having a higher refracting index. Correct?

Consider violet and red light through a rain drop. Both ligh pass equally as much and as diverse through the rain drop but the observer at a fixed location will only see both light when they constructivly interfere with themselves. For violet light, this means appearing closer to the normal of incidence because they will probably not have shown straight through but follwed a curved path due to colloisions hence have traveled a distance more than what it seems. For red light, it means further from the normal because they colloide less and have mostly shown 'straight on' through the material. Finally the distance both light have traveled should be about equal (although coming out at different locations and that is why we see chromatic dispersion).

Is this a correct explanation?

 

[inha]

Read the FAQ in this forum. It should get you started.

 

[berkeman]

Read the FAQ in this forum. It should get you started.

Is it mostly Post #4 in the FAQ that you are pointing the OP to? Or are there others? I tried a keyword search in that thread on "dispersion" but got no hits.

 

[pivoxa15]

I have read FAQ and have encorporated the new facts in my opening post. Does it sound right?

I am not sure about "...the observer at a fixed location will only see both light when they constructivly interfere with themselves." in my opening post.

 

[berkeman]

I don't think constructive interference has much of an effect with non-coherent natural light.

Rather, if you want to explore the frequency-dependent index of refraction phenomena (say, for different clear materials), one good way to do it is to make a thick block of the material, and shine a white light beam through at an angle. The thicker the block, the wider the linear displacement of the colors at the exit of the block. You could probably get a couple clear plastic blocks at the local plastic supply store to do some initial experiments and see if they match the n(f) published for the material.

 

[pivoxa15]

I don't think constructive interference has much of an effect with non-coherent natural light.

Rather, if you want to explore the frequency-dependent index of refraction phenomena (say, for different clear materials), one good way to do it is to make a thick block of the material, and shine a white light beam through at an angle. The thicker the block, the wider the linear displacement of the colors at the exit of the block. You could probably get a couple clear plastic blocks at the local plastic supply store to do some initial experiments and see if they match the n(f) published for the material.

I trust that it all works but my question is about the theory why the colours get dispersed.

 

[jtbell]

We really should have ZapperZ weigh in directly on this, but...

Quoting from his post #4 in the FAQ:

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

I draw your attention particularly to the sentence

This is similar to trying to oscillate something at a different frequency than the resonance frequency.

It is well-known that if you take a simple harmonic oscillator that normally oscillates at a natural (resonance) frequency \omega_0, and drive it with a force that oscillates at some other driving frequency \omega, it oscillates at the driving frequency, with a different phase from the driving force. The change in phase is not a constant amount, but varies with the driving frequency. Most students in the USA encounter this for the first time in a second-year university classical mechanics course. A good Google search might be for "driven harmonic oscillator", or "driven damped harmonic oscillator".

So, simplistically, if you consider a small section of the material (lattice), the outgoing light has the same frequency as the incoming light, but is shifted in phase by an amount that depends on the driving frequency. This has the same effect as if the wave had been delayed by an amount of time that produces the same phase difference. As the light travels through successive sections of the material, the phase shift accumulates, and has the same effect as a reduced wave velocity. The amount of phase shift per section of the material depends on the driving frequency, so the effective wave velocity also depends on the driving frequency.

 

[pivoxa15]

It is well-known that if you take a simple harmonic oscillator that normally oscillates at a natural (resonance) frequency \omega_0, and drive it with a force that oscillates at some other driving frequency \omega, it oscillates at the driving frequency, with a different phase from the driving force. The change in phase is not a constant amount, but varies with the driving frequency. Most students in the USA encounter this for the first time in a second-year university classical mechanics course. A good Google search might be for "driven harmonic oscillator", or "driven damped harmonic oscillator".

So, simplistically, if you consider a small section of the material (lattice), the outgoing light has the same frequency as the incoming light, but is shifted in phase by an amount that depends on the driving frequency. This has the same effect as if the wave had been delayed by an amount of time that produces the same phase difference. As the light travels through successive sections of the material, the phase shift accumulates, and has the same effect as a reduced wave velocity. The amount of phase shift per section of the material depends on the driving frequency, so the effective wave velocity also depends on the driving frequency.

Driving frequency is the frequency of the incoming light, which also becomes the frequency of the media(i.e. frequency of the lattice of atoms) after the light enters it?

How would you then link it with different colours becoming dispersed after passing through a different medium. Would you start by saying: Each colour have different driving frequency.

 

[berkeman]

Driving frequency is the frequency of the incoming light, which also becomes the frequency of the media(i.e. frequency of the lattice of atoms) after the light enters it?

How would you then link it with different colours becoming dispersed after passing through a different medium. Would you start by saying: Each colour have different driving frequency.

No, the driving frequency is the frequency of the incoming light, but the natural frequency of the media is a property of the media itself, independent of the light. Think of the natural frequency of the media like the natural frequency of a plucked guitar string.

And he was saying that the dispersion is a result of the different amounts of phase delay you get, depending on how far the light frequency is off from the natural frequency. (At least that's how I read it. Pretty interesting stuff!)

 

[pivoxa15]

No, the driving frequency is the frequency of the incoming light, but the natural frequency of the media is a property of the media itself, independent of the light. Think of the natural frequency of the media like the natural frequency of a plucked guitar string.

The driving frequency in this case would be the frequency of the pluck of string made by the player? Which could or could not be at the natural frequency of the guitar string. If not than the sound wouldn't sound as nice?

And he was saying that the dispersion is a result of the different amounts of phase delay you get, depending on how far the light frequency is off from the natural frequency. (At least that's how I read it. Pretty interesting stuff!)

Does the different changes in phase result in the waves bending by different amounts? In other words it accounts for them to travel in a different direction? How would that pan out in the wave equations?

What would happen if the driving frequency of a particular monochromatic light equaled the natural frequency of the media? There would be no change in phase? So it would like the new media is exactly the same as the old one?