Calculating Refractive Index of Liquid Mixtures: Is There a General Formula?

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Discussion Overview

The discussion revolves around the calculation of the refractive index of liquid mixtures, specifically addressing whether a general formula exists for mixtures of two liquids with known refractive indices, such as water and ethanol or water and glycerol. The scope includes theoretical considerations and approximations in the context of physics.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the existence of a general formula for calculating the refractive index of liquid mixtures, suggesting that the varying composition throughout the mixture complicates this.
  • Another participant proposes that averages could be used for calculations, indicating that refractive index may depend on density and suggesting the calculation of average density.
  • A different participant clarifies that a linear approximation can be used under the assumption of thorough mixing and constant composition, providing a formula for this approximation while noting it is not definitive.
  • It is stated that refractive index is not related to density, which challenges the earlier point about density dependence.

Areas of Agreement / Disagreement

Participants express disagreement regarding the existence of a general formula and the factors influencing refractive index, with no consensus reached on the matter.

Contextual Notes

The discussion highlights limitations related to assumptions about mixture composition and the applicability of approximations. The relationship between refractive index and density remains unresolved.

Ogulnius
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Is there a general formula to calculate the refractive index of a mixture of two liquids of known refractive index, e.g. water and ethanol, or water and glycerol?
 
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No. That is because a mixture is not a constant composition - the composition varies throughout the mixture. The index will be different at all these points.
 
O unless you want averages, then i guess so. Its been a while since I've done physics, but I think the refractive index is dependent only on density, and you can calculate the average density.
 
Of course, it is assumed that the liquids are thoroughly mixed and that the mixture is of constant composition.

As a coarse approximation you can use a linear formula:
n={ n_1V_1+n_2V_2\over V_1 + V_2 }
where n hold for the refractive indexes and V for the volumes.
But this is just an approximation.

Refractive index is not related to density.
 

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