# Refractive Index (RI) variation with Temperature & disagreement between two standards

I am comparing two different international standards for the same organic compound (clear and colorless liquid) and for the refractive index one standard says

1.531 to 1.534 (@ 20 °C)

The other one says

1.526 to 1.527 (@ 27 °C)

Now the ranges don't even overlap.

Couple of questions:

1. Would the change in testing temperature (20 °C vs 27 °C) be enough to explain this difference in standards? Would an increase in Temperature typically reduce the RI or increase it? By what percent per degree change in Temperature?

2. Any other testing intricacies for RI that I ought to be aware of? Is there a methodological / protocol difference that may explain this?

3. Is this a difference large enough to worry about? The difference in ranges is only about 0.3 %. What is the typical least count / accuracy of RI measurements in the lab?

• Are the refractive indices specified at the same wavelength? That alone could explain the difference. – Jon Custer Jan 4 '17 at 14:00
• @JonCuster Good point. Let me check the text of the standards. So far as I saw there wasn't explicit mention of a wavelength. Is there an assumed default? One standard was the US Pharmacoepea (USP-39) so quite an authoritative document. – curious_cat Jan 4 '17 at 14:14
• Usually at 589 nm, the sodium D2-line – Karl Jan 4 '17 at 17:40

The refractive index of a pure liquid varies with the wavelength of the light (this dispersion causes the splitting of white light into rainbow colours) and with the density and thus temperature of the liquid (this causes the schlieren patterns when heating a liquid on a hot plate).

The section “Index of Refraction of Liquids for Calibration Purposes”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL. lists values for several organic liquids at various wavelengths and temperatures.

Reference values close to the values given in the question can be found for toluene:

$$\textbf{Index of refraction of toluene}\\ \begin{array}{lll} \hline &\lambda/\mathrm{nm} &T=20\ \mathrm{^\circ C} &T=25\ \mathrm{^\circ C} &T=30\ \mathrm{^\circ C} \\ \hline &667.81 &1.49180 &1.48903 &1.48619 \\ &656.28 &1.49243 &1.48966 &1.48682 \\ &589.26 &1.49693 &1.49413 &1.49126 \\ &546.07 &1.50086 &1.49803 &1.49514 \\ &501.57 &1.50620 &1.50334 &1.50041 \\ &486.13 &1.50847 &1.50559 &1.50265 \\ &435.83 &1.51800 &1.51506 &1.51206 \\ \hline \end{array}$$

The uncertainty of the refractive index is estimated as $\pm0.00003$.

For example, the refractive index measured for toluene using the characteristic wavelength of a sodium-vapour lamp $(\lambda\approx589\ \mathrm{nm})$ at $T=20\ \mathrm{^\circ C}$ is $1.49693$. When increasing the temperature, the refractive index is decreased to $1.49413$ $(-0.19\ \%)$ at $T=25\ \mathrm{^\circ C}$ and to $1.49126$ $(-0.38\ \%)$ at $T=30\ \mathrm{^\circ C}$.

The range of values given in the question corresponds to a decrease between $-0.26\ \%$ and $-0.52\ \%$ when the temperature is increased from $T=20\ \mathrm{^\circ C}$ to $T=27\ \mathrm{^\circ C}$.

Electromagnetic waves are scattered at electrons, and refraction is interference of scattered waves.

The RI usually goes down with temperature, because it is proportional to the volume electron density in the substance.

So, yes, that looks OK with your two substances, if they are indeed identical. The absolute difference should be proportional to the thermal expansion of the material, 0.3% in seven centigrades sounds reasonable for an organic liquid (thermal expansion coefficient of e.g. ethanol $1.4\cdot 10^{-3}/$K, glycerol $0.52\cdot10^{-3}$/K).

• For solids, such a large volume change in only seven degrees would be pretty extreme (normal thermal expansion coefficients are given in units of $10^{-6}$/C). – Jon Custer Jan 4 '17 at 14:27
• @JonCuster Right, tnx. However the expansion coefficient of a liquid rises by typically two decades at $T_g$ . – Karl Jan 4 '17 at 17:36
• And the OP said 0.3%, not 1.3%, my typo. – Karl Jan 4 '17 at 17:47
• good points on liquids, particularly near transition points. – Jon Custer Jan 4 '17 at 19:22
• @JonCuster I think the expansion coefficient is typically rather constant between phase transitions. Water is afaik very unusual in that respect. – Karl Jan 4 '17 at 19:52