I understand this by the simple oscillator; when a force is applied to the object, it follows this force in the direction and magnitude.. but when the fore becomes larger and larger, the object has no time to follow the force and at some points it will be opposing the force. The same for light and electrons... electrons in atoms oscillates with a certain frequency and the incident light has a certain frequency as well. when the frequency becomes big the refractive index becomes less.

The first - almost always more than one !!!

Refractive index (n) is a ratio between the speed of light in vacuum (c) and the phase velocity of light in the material (vp); n=c/vp. In most cases vp1. But phase velocity can be sometimes bigger than c (e.g. for X-rays). In these cases n

Without repeating the above said part of explanation (which is equally important),

an idea of "group velocity refractive index"[“group index”] is also valid:

ng= c/vg

where vg is the group velocity.

Its wavelength dependence given as:

ng = n – λ. dn/ d λ

where λ is the wavelength in vacuum.

At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the permittivity of the medium. The charges will, in general, oscillate slightly out of phase with respect to the driving electric field. They radiate their own electromagnetic wave that is at the same frequency but with a phase delay. The macroscopic sum of all such contributions in the material is a wave with the same frequency but shorter wavelength than the original; leading to a slowing of the wave's phase velocity and thus lowering of [ng] value.

Sorry, folks, but the three comments (by Wasim, Marek, Manohar) all touch on the topic, but none are the answer (I think). Wasim describes a nonlinear behavior of the oscillating electrons in the material that are also mentioned, more correctly in my opinion, by Manohar: the oscillating electrons (in the classical approximation, considering electrons as infinitely small points of charge) achieve the same frequency   as the electromagnetic wave that sets them in motion. They then radiate their own waves, and these combine with the incoming wave. The phase between the incoming and the induced wave determines what the index of refraction is.

If the incoming wave oscillates relatively slowly, the electrons can follow the wave: they are in phase. So, what is 'relatively slowly'? This is in relation to the oscillation frequency of the electrons themselves: in this picture the electrons may be bound to some equilibrium position and oscillate back and forth around this location, always with a small enough amplitude that nonlinear effects can be ignored. Now, when the incoming wave's frequency exceeds that of the electrons, the electrons can no longer follow the wave, and they get out of phase. Then, the waves radiated by the electrons are out of phase too, and the index of refraction is less than unity.  

What Marek says is true, but not an explanation, it's a description. Mine is also a description but it describes the mathematics that models the underlying physics, in the classical approximation.

Interestingly, you can make lenses for x-rays with this refractive effect: they have been used on synchrotron radiation sources since 1996. In some ways the best material for these lenses is lithium metal, because for many interesting x-rays this material is little more than a bag of otherwise free electrons: one problem is that an electron bound to some equilibrium location can get into some higher energy state when you take quantum mechanics into account, and when it does the electron takes the necessary energy from the wave which is then absorbed. Not good, for a lens. 

I partly agree with respected Dr.Nino Pereira but with a humble addition- perhaps the exact explanation has to involve a mathematical treatment.And with all the limitations, I, at least, could not have thought of a better explanation regarding the nonlinear behaviour of oscillating electrons at the time writing the answer to this question. Yes; it is half done but have tried in my own way. Thks.

Manohar, you are quite right that the best way to react to the original question may have been 'sorry, the best way to explain it is with a little math', and then refer to basically any book on x-rays (including specifically the one by David Attwood on soft x-rays and EUV radiation), or maybe easier their web site (http://henke.lbl.gov/optical_constants/intro.html). But, what you say needs a correction: the index of refraction being less than unity, sometimes, is purely linear, everything is proportional to the amplitude of the incoming wave. Of course, as the amplitude increases you get nonlinear, and very interesting, effects, of different types (Kerr, filamentation, ...), too much to mention (and, also better explained through the math).

The index-of-refraction is a convenient way to describe wave propagation in a material that is electrically and magnetically polarized by the electromagnetic field of the propagating wave. For small fields the response of the material is proportional to the strength of the wave field.

In the case of x-rays, magnetic polarization is negligible but not the electric polarization which can be understood as an electric displacement field. The polarization of the material is frequency dependent and therefore quite different for x-rays than for, say, visible light. Also one should clarify that usually the index-of-refraction is understood as a complex quantity. The imaginary part describes absorption of the x-rays. The real part is the matter of discussion here and in fact is almost always slightly smaller than one for x-rays. This is equivalent to a negative electric polarization of the material in response to the wave field. So physically the material response is in opposition to the excitating wave field.

The next question would be: Why is the material response in opposition to the exciting wave field?-  This behavior requires a microscopic model of the material. A simple model is the mentioned Lorentz oscillator which captures the observed effect if its resonance frequency is much lower than the frequency of the x-ray wave field.

Note: If the material has nuclei with transitions matching the x-ray energy a nuclear resonant excitation occurs, and the index-of-refraction can assume values larger than one close to the resonance.

Exactly: whenever there is a resonance funny things happen, including absorption and the description of it by an index of refraction that is complex. Happens too in the optical.

if n

Just a brief comment - after that the discussion is mostly over, I think.

Rather recently I encountered this issue from a need to determine porosity of thin layers from 'Xray grazing incidence measurements'. I learned that it was about 'total internal reflection'.

How?! The initial impression was that this couldn't be real.

After contemplating and some consulting I concluded that at least for me personally, the idea that the Xrays are interacting with electrons above their 'resonance frequency' is a satisfactory picture. And in need I will be happy to go through the maths in depth.

Disregarding other kinds of interactions, a pretty strong conclusion is then that every material has this property!

Extrapolating this line of thinking one may think about the plasma frequency of the ionosphere. At some point in the broadcasting frequency range (TV?) the transmitted waves are supposed to leave earth into space. But this phenomen should still work, right? At sufficiently shallow angles? And the final question:

Is this the explanation for that hi frequency communication sometimes can propagate very long distances (not to be confused by standard 'reflection' of short wave com exercised by ham amateurs)? Eg, sometimes Custom staff in Italy can be heard in Sweden!