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I have taken some measurements of refractive index (refractometer (commercial Brix meter), nD20 i.e. 20 degrees C and 589 nm) and density of sucrose/water mixtures and also of ethanol/water mixtures.

For non-mixtures, the Lorentz-Lorenz equation predicts: $$ \frac{n^2-1}{n^2+2} = \frac{\alpha}{3\epsilon_0} \frac{N_A}{M}\rho$$

For mixtures, Lorentz neglects inter-particle interactions and suggests to add the contributions by their volume fractions: $$\frac{n^2-1}{n^2+2}=\sum f_{V,i}\frac{n_i^2-1}{n_i^2+2}$$

Here are my results: Lorentz-Lorenz relation plot

I added some values I found in a technical note of an equipment vendor. The "slope" lines are just straight lines drawn between the origin and the points corresponding to literature values for water and sacharose.

If I squint, my measured results are not completely far off the Lorentz model prediction. But, I also notice that I am systematically underestimating the measured refractive index of the mixture with the model prediction.

It seems reasonable that the no-interaction assumption is incorrect. I see “dipole coupling” mentioned on the internet. Sounds reasonable for the things I’m mixing. Unfortunately I haven’t been able to find or figure out how to correct the Lorentz-Lorenz model.

How would I go about doing that?

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    $\begingroup$ Nice question! I think a crucial point is: what is the polarizability $\alpha$ and how do you calculate it? One thing I can recommend is to look for "linear dispersion theory". In my understanding, Lorentz-Lorenz is a highly simplified form of this. $\endgroup$ May 4, 2023 at 7:03

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