index of refraction

[riseNshine]

Why does the index of refraction increase with increasing frequency if n=c/v and hence n=c/(wavelength*frequency).

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[bored]

you sure what you have is a true statement?
doesn't it seems like the n should decrease.

 

[dontbeanegaton]

Remember that the frequency does not change in a medium. Only the wavelength changes. The easiest way to conceptualize this is to think about the fact that if light is striking a surface of, say, water, the crests will hit the surface with a frequency. Inside that water, those crests have to be transmitted at the same rate, since the water has to "process" that number of crests no matter what.
In other words, its like you are scrunching the wave. It travels slower, but at both interfaces it has to "process" the same number of crests every second.
In mathematical terms, that means if n gets larger, the value of v = f*wavelength must get smaller. Since only wavelength changes, the wavelength is reduced.
Another way to think about it is that frequency corresponds to the energy of the light particle. The energy, and thus the frequency, won't change when you switch mediums.

 

[ebasappa]

Remember that the frequency does not change in a medium. Only the wavelength changes. The easiest way to conceptualize this is to think about the fact that if light is striking a surface of, say, water, the crests will hit the surface with a frequency. Inside that water, those crests have to be transmitted at the same rate, since the water has to "process" that number of crests no matter what.
In other words, its like you are scrunching the wave. It travels slower, but at both interfaces it has to "process" the same number of crests every second.
In mathematical terms, that means if n gets larger, the value of v = f*wavelength must get smaller. Since only wavelength changes, the wavelength is reduced.
Another way to think about it is that frequency corresponds to the energy of the light particle. The energy, and thus the frequency, won't change when you switch mediums.

Best explanation ever

 

[riseNshine]

I understand that explanation, but I'm confused because I saw this in the princeton review science review questions/solutions: #105:

What is dispersion? How does the index of refraction depend on the frequency of the light?

Answer: Separation of individual colors (frequencies) of a beam of light due to the small dependence of refractive index on frequency. Higher frequencies have higher indices of refraction.

Is a dispersive medium an exception where within the medium, they travel at different frequencies?