# Refractometer principles

## Refractive index

Every material with which light interacts has a refractive index (RI, symbolized as n). This constant, dimensionless number describes how fast light moves through a specific medium, in relation to how fast it moves through a reference medium (usually vacuum or air). The lower the optical density of the medium, the higher the speed of light inside the medium and the lower its refractive index.

### Examples of the speed of light in different media

 Vacuum 299 792 km/s Air 299 710 km/s Water 225 000 km/s Sapphire 170 000 km/s

The refractive index of a substance is dependent on the wavelength λ of the light and the temperature T of the substance. Reference to the refractive index must therefore also specify the wavelength and temperature, when the measurement is not done under standard conditions.
The standard wavelength for refractometric measurements is 589 nm these conditions, the refractive index (n) is often written as nD or nD.

Several refractive index scales are in use.
The absolute refractive index of a medium is the ratio of the speed of light in vacuum relative to the speed in the medium.
While this is the most fundamental definition, it is more common to use the refractive index relative to air.
Since the (absolute) refractive index of the medium of interest as well as the refractive index of air depend on temperature, it is necessary to specify the details.

Common variants are:

– the temerature dependent refractive index of the medium relative to standard air, that is air at 20°C, 1013hPa, and 50% relative humidity
– the temerature dependent refractive index of the medium relative to air of the same temperature

### Examples of different refractive indices

(wavelength = 589.3 nm, temperature = 20.0 °C)

 Sample nD(T=20°C) relative to vacuum nD(T=20°C) relative to standard air Vacuum 1.00000 0,99973 Air 1,00027 1,00000 Water 1,33335 1,33299 Dodecane 1,42211 1,42172 Tetrachloroethylene 1,50621 1,50580 Bromonaphtalene 1,65829 1,65784 Sapphire Al2O3 1,76 1,76 YAG 1.83 1,83 Diamond C 2.42 2,42

## Measuring principle of refractometers

The operation of the refractometer is based on the physical principle of light refraction (Snell’s law). Light slows down as it passes into more optically dense media, and speeds up as it passes into less optically dense media. The change in speed is accompanied by a change in direction, and at a certain angle of incidence, the light does not refract in the second medium at all, but is entirely reflected. The angle at which this occurs is known as the critical angle, and it is this angle that the refractometer measures.

An easy way to visualize this phenomenon is in terms of the perceived and actual location of a fish below the surface of a body of water. The refraction of light leaving the water and entering the air causes us to perceive the location of the fish as closer than it actually it.

A refractometer consists of a light source, filtered to a single wavelength, which is directed towards the prism-sample interface by a converging lens. This creates a range of incidence angles, some of which (those less than the critical angle) will be completely reflected. A Charge-coupled Device (CCD) sensor precisely measures the intensity of the reflected light and determines the exact angle αcritical at which light begins to be completely reflected. Because this angle is dependent on the ratio of the refractive index of the prism to that of the sample, the refractive index of the sample can be determined using the known refractive index of the prism.

## Snell´s Law

In this diagram, beam A strikes the interface of medium 1 (with refractive index = n1) and medium 2 (with refractive index = n2, where n2 > n1) at the incident angle α1. This results in the partial reflection (beam A’) and partial refraction (beam A at angle β1) at the boundary surface.

At a certain angle of incidence α2, one part of the light beam is reflected and another part is refracted exactly along the interface of the two media. This is known as total reflection and the angle is referred to as the critical angle of total reflection.

When the beam is incident at an angle greater then αcritical, the light beam will be entirely reflected (beam C’).

Snell’s law can be applied to determine the RI of medium 1. The law states that the ratio of the RIs is equal to the inverse ratio of the sinus of angles α1 and β1.

When α2 = αcritical, the angle α1 = β1 = 90°. Substituting these values into Snell’s law gives

Measuring the RI of medium 2 and the critical angle of total reflection αcritical can therefore yield the RI of medium 2.

## Schematic setup of an Abbemat Refractometer

Figure 1 illustrates the resultant step in light intensity, as measured by the CCD sensor, which is used to determine the critical angle. A theoretical “Fresnel” curve is applied to the video signal taken with the CCD sensor, which allows for the objective determination of the critical angle. This technique guarantees a more accurate and reliable determination of the refraction index compared to simple shadow line detection.

## Refractive index’s dependence on wavelength

For almost all materials, the refractive index differs for different wavelengths, in a pattern characteristic to each material. This is known as the dispersion relation.

Figure 4 illustrates the absorption (blue curve) and dispersion relation (red curve) of water, over a range of wavelengths. The refractive index drops through the visible spectrum into the beginning of the infrared, while nearly no absorption is seen in this range.

In order to accurately determine the refractive index of a sample, it is therefore necessary to ensure the precision of the wavelength with an interference filter. While most refractometric measurements are done at 589 (or 589.3) nm, the wavelength of the sodium D-line, some applications require other wavelengths.

The industry standard use of the 589 nm wavelength is a historical throwback to sodium lamps being widely available as a cheap and reliable light source. The name “D-line” refers to the symbol given to the spectral line of sodium by Joseph von Fraunhofer, the German physicist credited with the discovery and mapping of over 570 spectral lines.

## Refractive index’s dependence on temperature

Temperature is another major influence on refractive index and must therefore be precisely controlled and measured during the entire procedure. While older instruments often employ a water bath for this purpose, newer instruments often have the option to use more precise Peltier temperature controls. High-precision temperature controls stabilize the temperature of both the sample and the measuring prism, and are paired with highly accurate temperature sensors.

## References

• Tilton, L. W. and Taylor, J. K. (1938).
Refractive index and dispersion of distilled water for visible radiation at temperatures 0 to 60 °C. J. Res. Natl. Bur. Stand. 20, pp. 419-477.
• Haynes, W. M., Lide, D. R., Bruno, T. J. (2015).
CRC Handbook of Chemistry and Physics, 96th Edition. CRC Press Taylor & Francis Group.
• W. M., Lide, D. R., Bruno, T. J. (2015).
CRC Handbook of Chemistry and Physics, 96th Edition. CRC Press Taylor & Francis Group
• RI Dodecan, Tetrachloroethylene, Bromonaphtalene:
PTB (Physikalisch-Technische Bundesanstalt, Braunschweig) Standards