neelakash,
You are not correct.
You should first define what you call the refractive index.
A general definition of the refractive index is obtained from:
- the wavevector (k) of a wave propagating in the given medium
- the frequency ([tex]\omega = 2{\pi}f[/tex]) of the same wave
the definition is:
[tex]\mathbf n = \frac {\mathbf{k}}{\omega}[/tex]
as you can see, it is a vector, in general.
This vector is the same for all directions in isotropic materials.
Note that it might depend also on the polarisation of the wave.
Now the crucial question is: how do you get the wavevector (k) ?
The answer is simple: solve the Maxwell's equations.
In the Maxwell's equations, you need to include the currents and the charges as well as the external excitations and boundary conditions. The internal currents and charges are related to the wave-fields. When the motions of the electric charges are small enough, and the response of the medium to the excitation can be assumed as a linear response, then the dielectric tensor gives the link between the excititation and the response of the medium. When solving the equations, there is usually no stationary solution (solution is zero!) unless the (linear) equations satisfy a certain equation called the dispersion relation that has (for linear systems) the general forme f(k,w)=0 .
In non-isotropic media, there are usually several solutions to the dispersion relation. These different solutions are sometimes called modes or branches or simply the xxxx-wave (xxxx can be any wave name!). For each of these modes the refractive index can be calculated.
Of course, in isotropic media, all these things are much simpler. So much simpler that the refractive index looks like a primary concept, while actually it is not really a primary concept. the primary concept is the concept of response of the electric charges to an excitation. For small responses (linear assumption, very oftne a valid assumption), the dielectric tensor represents this link between response and excitation. For very simple system, the dielectric tensor is the refractive index. In general, there is a longer way from the dielectric tensor to the refractive index.
Finally, let me indicate that the response of the electric charge depends on the frequency of the exciting wave. For example, heavier charges (ions) cannot respond as fast as electrons. Therefore (in plasmas) very high frequencies with excite electron motions but not ion motions. Many other effects can give a big role to the frequency. I like the case when there are external magnetic fields: in this case the wave can be resonant with the rotational motion of charged particle around magnetic field lines, this leads to so-called cyclotron waves (io- or electron-). In condensed media the atomic and molecular structure plays a very complicated role, not to mention also semiconductors. Therefore, it should be no surprise that the refractive index depends on the frequency, since the refractive index depends on how charged particles respond to the exciting field.
To be very clear:
The dieletric tensor (or constant) does really depend on the frequency, but also on other things, like the direction of the wave.
The refractive index is related to the dielectric tensor and does therefore also depend on the frequency.