N=c/v=λ0/λ (T doesn't change) and v of light is constant

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n=c/v=λ0/λ (T doesn't change) and v of light is constant in a specific medium(i.e. the ratio is constant in given mediums), so the index of refraction is constant for all light when changing mediums.

If we say that index of refraction differs according to the wavelength, then there is contradiction with the above formula n=c/v that says n is constant in specific medium
 
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what i meant to ask is that the formula n=c/v shows that the index is constant for all light and depends only on the medium. however while explaining the dispersion, they say that the index of refraction depends on the wavelength of every light.

isn't there a contradiction?

thanks for answering
 


The phase velocity of the material, v, is dependent upon the wavelength.
 


Born2bwire said:
The phase velocity of the material, v, is dependent upon the wavelength.

do u mean that the velocity of light in a specific medium is not constant and differs according to the wavelength?

for example do x-rays and radio waves have different speeds in glass?
 


brainyman89 said:
do u mean that the velocity of light in a specific medium is not constant and differs according to the wavelength?

for example do x-rays and radio waves have different speeds in glass?
Yes. You don't even need to go that extreme; violet and red wavelengths have different speeds in glass.

Here is a graph of n vs. λ for several different types of glass: visible wavelengths are shown by the pink band:

dispersion-curve3.png