Speed of EM wave depending on the frequency

[synMehdi]

I know that in a vacuum, speed of light is constant. My question is more about the speed of light in a material like air. Dispersion of light in a prism tells us that the speed of light or the material index depends on the wavelength ( or frequency which is constant ) so I thought that air induces also a dispersion in EM waves. If true, I want to know if there is a relation between velocity of EM waves and frequency in air. my aim is to calculate speed of light for different frequencies (radio frequencies) in air.

 

[SteamKing]

It's not clear exactly what your goal is here. The speed of propagation of an EM signal is constant in a given medium and is a maximum in a vacuum.
Since the speed is constant, when the frequency of an EM signal changes, the wavelength of the signal changes such that the speed of propagation remains a constant.

 

[synMehdi]

Thank you for your response.
If speed of light is constant in a given medium, why do we have dispersion? I'm confused, I thought that blue light traveled slightly faster than red light.

 

[Meesh]

It is constant within the medium. You want to look at the refractive index (n). In air, n=1. In a prism, it depends on the glass but generally, the more dense the medium the higher the refractive index (water: n=1.33 or something). I'm not sure about exactly at the point where the light bends but since the velocity changes (very quickly) I guess there is an acceleration of the particles, just so fast that it is neglected (at least for now...). You can find a lot of information on this topic by searching "refractive index" or "refractive index of a prism" or "refractive index of a gas"... Other than that you could search " speed of light in a medium".

Velocity = c/n
Where c = the speed of light. Although this is the equation I have in my notes, I believe there is a more complex one (as in add the wavelength of the light) that I didn't write down (as it was unimportant at the time - we were writing review for a man looking at a fish in water and the light from the fish to his eyes was bent... Where is the fish actually at time t compared to where the man actually sees him? ) I hope this helps. :)

 

[blue_leaf77]

$v = c/n(\lambda)$. For a given material, the mathematical expression of $n(\lambda)$ is usually given in a form of fitting equation which is called Sellmeier's equation. This equation will give close values to those observed experimentally only within certain frequency/wavelength range.

By the way if the light you are talking about is monochromatic then there is no dispersion in any medium, and for normal dispersion blue travels slower than red.

 

[Meesh]

Sorry update: the refractive index is independent of the wavelength that was a silly mistake on my part. The equation I gave you is universal. Basically the wavelength of your light changes inside the medium ( lambda = lambda naught/n ) where lambda is the wavelength and lambda naught is the wavelength before entering the medium.

A cool experiment if you have access to a green laser and vegetable oil, is fill a clear cup or glass with the oil and shine your green laser into the top of the oil. You notice that inside the oil, the green laser is actually now orange because the refractive index was so high that the change in wavelength was so much to make a noticeable change in colour inside the medium. This is also why you see the rainbow effect in a prism.

 

[synMehdi]

Thank you both for taking the time to answer.
So speed does changes depending on the wavelength but I couldn't find Sellmeier's parameters in air. My aim is to calculate speed of light in distant wavelengths in radio spectrum. I also know about Abbe number but I think it is used only in visible light spectrum.

 

[blue_leaf77]

I'm not quite sure if dispersion can become that severe in radio frequencies. Usually people working in low frequencies only take the DC permittivity for the refractive index, i.e. constant. Note that you might begin to think dispersion as a serious problem once the bandwidth of the signal is such that signal in time domain approaches few-cycle in duration. If you still insist on looking it up, I suggest that you go to electrical engineering section of this forum in hope that antenna guys will notice. Just give your thread a more purpose-indicating title.

 

[Meesh]

I agree. Something along the lines of radio frequency of a wave through a medium. Or something. You may want to start looking just purely at the em side of that though instead of light. Maybe take a look at Gauss's law and properties of a traveling wave. Sorry I couldn't come up with a sufficient answer. If I do I will post it though.