Dispersion/Refraction, but WHY?

[mjcguest]

I understand and have seen light disperse as it shines through a prism, crysal or other medium; I have seen snells law, I have searched this forum for answers..!

But I can not find an explanation I can understand of *why* a shorter wavelength of light will bend differently to a longer wavelength? What is the nature of the interaction or the nature of the wave that causes the bend, and why would the wavelength be the determining factor?

Thanks in advance for the newb-busting answer!
Matt

 

[tiny-tim]

Hi Matt!

It's the speed of the light that determines it …

the index of refraction is the ratio of the speeds before and after …

and the speed happens to depend on the wavelength.

(why? well, that's quantum mechanics for you! … something to do with the way the light interacts with the molecules. )

 

[mjcguest]

Thanks Tim. You've sort of highlighted the question... I have access to plenty of text that tells me what will happen, but nothing I've found that tells me why?

 

[James Leighe]

Thanks Tim. You've sort of highlighted the question... I have access to plenty of text that tells me what will happen, but nothing I've found that tells me why?

The why is usually harder than the what.

EDIT: I was looking for some link to give you a better intuitive idea of what is going on when a wave interacts with the 'boundary' but I can't find anything!

 

[Andy Resnick]

Ultimately, Physics cannot answer 'why'. We sometimes describe observations and sometimes make predictions. We observe dispersion, we have reasonably good models, and we can predict the dispersion for some simple materials. That's as good as it gets.

 

[Point Conception]

At the microscale an electromagnetic wave is slowed in a material because the electric field
creates a disturbance in the charges of each atom - primarily the electron proportional to the permittivity.
The oscillation of charges itself causes the radiation of an electromagnetic wave that is
slightly out of phase with the original wave. The sum of the two waves creates a wave of
the same frequency but shorter wavelength than the original leading to slowing of the waves travel.
* An electron in an atom or molecule is bound there by strong restoring forces.It has a
definite natural frequency.For electrons in atoms it is usually in a region corresponding to
violet or U.V. light. In mechanical systems it is possible to "drive" the system most
effectively if we impress on it an external force whose frequency is as close as possible to that of the natural resonate frequency.In the case of light the blue is closer to the natural
resonate frequency of the bound electrons than red light. Therefore we would expect the blue light to be more effective in causing the electrons to oscillate.

last paragraph referenced from Physics, Halliday-Resnick

 

[jtbell]

nothing I've found that tells me why?

I guess you haven't checked out the Physics Forums FAQ at the top of this very forum?

(in particular post #4)

 

[mjcguest]

I guess you haven't checked out the Physics Forums FAQ at the top of this very forum?

(in particular post #4)

I have - and it's gives a superb explanation of the change in speed; but I can't see anything that explains why the angle of refraction changes in relation to the wavelength

Any pointers to layman-friendly sources would be gratefully receieved!

Thanks
Matt

 

[Doc Al]

I have - and it's gives a superb explanation of the change in speed; but I can't see anything that explains why the angle of refraction changes in relation to the wavelength

What matters is the change in speed, which of course changes the wavelength. When a wave encounters a medium (of higher index of refraction) it slows down. If it meets the boundary at an angle, the change in speed will cause different parts of the wave to slow down at different times, thus changing the direction of the wave. See: http://www.physicsclassroom.com/Class/refrn/U14L1e.cfm"

 

[Andy Resnick]

What matters is the change in speed, which of course changes the wavelength. When a wave encounters a medium (of higher index of refraction) it slows down. If it meets the boundary at an angle, the change in speed will cause different parts of the wave to slow down at different times, thus changing the direction of the wave. See: http://www.physicsclassroom.com/Class/refrn/U14L1e.cfm"

I relaize this is a stock answer, but possibly confusing to the student- there is a steady stream of 'how does one part of the wave know what the other part is doing?' type questions here.

Better (IMO) to simply say that the momentum changes, so the direction changes.

 

[Doc Al]

I relaize this is a stock answer, but possibly confusing to the student- there is a steady stream of 'how does one part of the wave know what the other part is doing?' type questions here.

You're right, there's a good bit of handwaving here. But I think the argument can be made at least semi-rigorous by invoking Huygen's principle and detailing how wavefronts are defined.

Better (IMO) to simply say that the momentum changes, so the direction changes.

Can you expand on this?

 

[Bob S]

Morrowbay's post #6, including the quote from Halladay & Resnik, describes the dispersion caused by the atomic electric dipole resonances and anomalous dispersion (see http://en.wikipedia.org/wiki/Dispersion_(optics )
usually in the UV region, where the index of refraction, which normally increases with decreasing wavelength, suddenly increases very fast, and then decreases very fast (the anomalous part), diving below n=1. The phase shift described by morrowbay is identical to the phase shift observed in RLC electric circuits, when driven off-resonance.
Bob S
[Edit] See also discussion in Section 7.5 in Jackson "Classical Electrodynamics" (second edition) on frequency dispersion.

 

[Andy Resnick]

You're right, there's a good bit of handwaving here. But I think the argument can be made at least semi-rigorous by invoking Huygen's principle and detailing how wavefronts are defined.

Can you expand on this?

Sure-
http://www.iop.org/EJ/article/0031-9120/35/5/310/pe0510.pdf?request-id=229de04f-40ae-4082-8189-f4e9ffae82b1

The article mentions use of this model for photons, but it works for rays as well.

 

[Doc Al]

Hey, I like it. Thanks, Andy!