good question

Yes, there is . May be find it in matlab mathwork.

There are several theoretical approaches to the topic (known as effective medium theories). I know of no software ready for you to do such a calculation. You will have to study what is appropriate for the case you're interested in.

A good starting point is Chapter 4.5 in the book by O. Stenzel: The Physics of Thin Film Optical Spectra. In there, you will find some discussion of the topic.

https://www.researchgate.net/profile/Jerome_Polesel/post/What_is_the_correct_band_gap_determined_by_a_Tauc_plot/attachment/59d620fc79197b807797f6da/AS%3A293973668188172%401447100192588/download/The+Physics+of+Thin+Film+Optical+Spectra_+An+Introduction.pdf

Adding to Kai,

In order to get the refractive index you can also obtain it through the relative dielectric constant of the material. It is so that the refractive index n = sqroot of epsilonr. So, if the dielectric connsatn of the material is measured in the optical frequency then you can use it. I think there are expressions for the dielectric constant of the material related to its chemical structure defining its portability.

Best wishes

Respected all Sir,

I want to know also that the mixture refractive index have a common formula or different for different materials. Also how many physical and chemical parameters that can affect the refractive index.

Dear Abdelhalim Zekry,

effective medium theories actually are theories for the effective (complex) dielectric function (or (complex) optical polarizability) of inhomogeneous, composite media.

If you do good measurements (on hopefully well defined samples) then of course you can in principle derive the correct, effecive dielectric function or refractive index for that material, at least when the inhomgeneity occurs on length scales well below the wavelength. [It should be added, that contrary to many statements that can be found on RG, the retrieval of the optical response functions from measurements such as e.g. transmission and/or reflectivity of thin films is not a trivial task, there are no valid direct analytical expressions (formulae) for doing that.]

This, however was not the question. It was rather: given the known optical response of two materials, what is the response of their mixture? Which brings us back to the effective medium theories and that you need to analyze your situation carefully in order to know how to apply them. There is no a priori, ready to go universal formula.

Dear Arvind Sharma,

the (complex) refractive index contains no other information than the complex dielectric function which in turn is (1+poarizability). For all practical purposes this is given by the interaction of the electromagnetic radiation with all excitations in the solid that couple to it (such as ionic vibrations or electronic transitions).

Now you have a mixture of two materials. This has several consequences: the small pieces of materials may (and usually will) have different optical properties than the corresponding bulk material due to "size effects" (such as quantum confinement) and probably modified composition at their surface (which actually forms an interface in the material). If the mixture is disordered then either you will have a porous material (reducing the average polarizability) or some grain boundary material which will be different from either of the two constituents.

Effective medium theories provide you with the best ideas people have come up with to describe the mixture on the basis of the known optical constants of its constituents. As with any theory, each of them has their limitations in terms of applicability and accuracy.

You cannot escape studying the corresponding literature if you want to understand what this is all about and why there is no general (or even simple) formula without severe limitations.

I did't know how to calculate refractive index of a composite of nanoparticles. can anyone help me?