Other answers are either mathematically formal or critical of you personally for even asking the question.  Let me try to be a little more helpful by providing what I hope will be an intuitively meaningful answer.  Consider a material like glass (mostly SiO2) that has some impurity (like sodium, Na, which is added intentionally, so not exactly an impurity, but never mind that detail).  As I'm sure you know, Na strongly emits (in a flame or a discharge) a bright yellow light; you probably also know that if it emits light of this color it also absorbs it.  In the glass there's not much opportunity for it to emit, but it can (and does) still absorb it.  But then what? Usually it will re-emit it, after a short delay.  This delay affects the macroscopic (apparent) velocity of light in the glass, which is a (reciprocal) measure of the index of refraction.  The closer the wavelength of the light to the color of this "resonance" the longer the delay, the smaller the apparent velocity, so the larger the index of refraction.  Of course this intuitive model runs roughshod over all sorts of wave/quantum mechanics concepts, i.e., it oversimplifies crucial concepts like phase shift, but I hope that with this simple "mechanical" model in mind, maybe it will be easier for you to follow up on the references others have given and eventually understand what is happening at a deeper but unavoidably more formal level.

Both can occur but in general refractive index of all material can be varied with wavelength and each material have it's specific behavior. but some optically active material changed their optical properties with specific light emission.  

Please find attached a short introduction to the dispersion of refractive index:

http://www.us.schott.com/advanced_optics/english/download/schott-tie-29-refractive-index-and-dispersion-april-2014-us.pdf

http://course.ee.ust.hk/elec342/notes/Lecture%207_absorption%20and%20dispersion.pdf

The dispersion becomes significant of the wavelength approaches an absorption band

Other answers are either mathematically formal or critical of you personally for even asking the question.  Let me try to be a little more helpful by providing what I hope will be an intuitively meaningful answer.  Consider a material like glass (mostly SiO2) that has some impurity (like sodium, Na, which is added intentionally, so not exactly an impurity, but never mind that detail).  As I'm sure you know, Na strongly emits (in a flame or a discharge) a bright yellow light; you probably also know that if it emits light of this color it also absorbs it.  In the glass there's not much opportunity for it to emit, but it can (and does) still absorb it.  But then what? Usually it will re-emit it, after a short delay.  This delay affects the macroscopic (apparent) velocity of light in the glass, which is a (reciprocal) measure of the index of refraction.  The closer the wavelength of the light to the color of this "resonance" the longer the delay, the smaller the apparent velocity, so the larger the index of refraction.  Of course this intuitive model runs roughshod over all sorts of wave/quantum mechanics concepts, i.e., it oversimplifies crucial concepts like phase shift, but I hope that with this simple "mechanical" model in mind, maybe it will be easier for you to follow up on the references others have given and eventually understand what is happening at a deeper but unavoidably more formal level.

Basically, It is depend upon the band gap of the material. It s the light and matter interaction. 

Very shortly.

The light-material interaction depends on the nature of material and on the light wavelength.

Yes, it is true. 

we can't say both, is only the nature of material which define you light-matter interaction.

what you have to know is: the refractive index quatify  the velocity of the light in your material relativly with the same velocity at the vaccum.

the light is also a combination of an electrical and magnetic field (electromagnetic wave), both of them can be propagated, absorbed...... in your material, all of this propreties were include in  your refrective index. and the propagation, absorption.... depend on your nature of material...

One could ask the same question with refractive index replaced by the impedence of some alternating current circuit element (say a coil) and the light frequency replaced by the frequency of an applied alternating current. The logic of what depends on what remains the same (actually the involved physical processes are closely related).

This is a wonderful question because it is really at the heart so many physical processes.  My succinct, but possible perplexing, initial answer is that, "there is no such thing as an ideal bandpass filter."  In this light, I think of a lumped circuit.  In order to create a truly spectrally flat bandpass filter, one needs an infinite number of inductors and capacitors (resonances=poles).  If you accept this claim, then it is obvious that a truly spectrally flat response is simply not possible for a circuit, as it would take up an infinite area....Now jump ahead to materials in the optical domain.  You are essentially asking why don't materials respond the same way to all frequencies, i.e, why does the refractive index (real and imaginary parts) depend on frequency.  In order for a material to respond without preference to any frequency would mean that the material would behave as an ideal band pass filter (or band stop) filter.  This necessitates an infinite number of poles (or zeros).  While poles in the circuit domain are associated with lumped LC resonances, they are associated with quantum mechanical transitions in the optical domain, i.e., electrons being excited/relaxed.  In the end I would flip your question on its head and ask:  Is it possible to create a (meta)material with a frequency independent complex response from IR to UV?  I don't think it is but I would love to be wrong.