## Refractometers – Measuring Principle

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This section contains some information about the basic principles of refractive index measurement.

## What is Refractive Index?

Refractive Index n is the speed of light in vacuum relative to the speed of light in the considered medium:

n = speed of light in vacuum / speed of light in medium

Example:
Water has a refractive index of 1.33 which means that the light travels 1.33 faster in vacuum than in water.

### Snell’s law When light enters from a medium with a lower refractive index as for example air into a medium with a higher refractive index as for example water it thus changes its speed. This has as a consequence that a beam of light changes its angle when it passes from one medium with a refractive index n1 to another medium with a refractive index n2. The ratio of the sines of the two angles is equivalent to the opposite ratio of the refractive indices of the two media. This mathematical relationship is known as Snell’s law.

### Influence of temperature and wavelength The refractive index depends on the temperature of the media: The higher the temperature of a media, the higher the speed of light in the media and the lower its refractive index. The picture below shows the refractive index of water in relation to the temperature.

In vacuum light travels at a constant speed (c), independent of its wavelength. In all other media, however, the speed of light depends as well on its wavelength: The shorter the wavelength of the light, the higher its speed. This frequency dependency of the refractive index is known as dispersion and causes a prism or a rainbow (where the light travels from air through water) to divide white light into its constituent spectral colors.

The refractive index has thus always to be stated together with the wavelength of the light used for the measurement and the temperature of the media. The refractive index is normally measured at a temperature of 20°C using light with the wavelength of the sodium D line (589.29 nm) and is therefore expressed as nD20.

## How does a Digital Refractometer work? In digital refractometers the light (1) travels from a prism (2) with a high refractive index (normally glass or artificial sapphire) into the sample (3). If the angle of incidence exceeds a certain value, the light is reflected at the prism/sample boundary (see ‘total internal reflection’ in the chapter above). The reflected light is detected by a CCD (or CMOS) sensor (4): The lower the refractive index of the sample being measured, the smaller the critical angle and the bigger the illuminated surface of the sensor. The refractive index of the sample can thus by calculated by the refractometer, using the ratio of the length of the illuminated and the length of the dark region on the CCD. Under ideal conditions a sharp transition dividing the dark and the light areas is yielded on the CCD. When measuring turbid samples, however, part of the light is reflected by the particles in the sample. The same can happen if the prism of the instrument was not clean when the sample was applied (non homogeneous sample on the surface of the prism) or if too few sample was used for the measurement (total reflection of light at the interface sample/air!). A part of this so called scattered light hits the CCD as well causing a blurry transition dividing the dark and the light areas on the CCD. Scattered light reduces the accuracy of the reading and is one of the most frequent sources of error when performing refractive index measurements. The pictures below illustrate the measurement of a clear (no scattered light, left) and a turbid (scattered light, right) sample.

When measuring turbid samples with optical Abbe refractometers, this blurry transition can easily been seen. With most digital refractometers, however, this is not the case: They simply give a non accurate reading.

In order to avoid this problem, the KEM RA-600 and RA-610 refractometers are equipped with a so called Abbe View: The light / dark transition appears directly as an image on the display of the instrument. It is thus easy for the operator to get aware of scattered light and to react accordingly by either filtering the sample prior to measurement or by cleaning the surface of the prism.

As the refractive index depends on the wavelength of the light (see chapter above), normally a light emitting diode with interference filters is used in order to get light with a wavelength of 589.29 nm.

The refractive index is as well temperature dependent and must therefore be determined at a well defined temperature (normally at exactly 20°C). Two approaches are possible:

• The samples are thermostated. In the past, circulation water bath thermostates were used for this purpose. In the year 1994 KEM launched the first digital refractometer equipped with a solid state thermostat available in the market. It is important to know that it takes a while until the temperature distribution in the sample is homogeneous once it is applied to the measuring cell. In order to shorten the time required per measurement, KEM refractometers are equipped with several temperature sensors (measuring the temperature of the prism, the block and the ambient). This makes it possible to calculate and adjust the (decisive) temperature at the sample / prism interface accurately much before the temperature distribution in the sample is completely homogeneous.
• Portable refractometers cannot be equipped with a thermostat. With such instruments, the samples are measured at ambient temperature. The sample temperature is recorded and the result of the measurement is converted to a temperature of 20°C by calculation using a temperature compensation coefficient (⍺). The temperature compensation coefficient depends on the nature of the sample. To get reliable results it is therefore important to use the correct temperature compensation coefficient to convert the result to the reference temperature. For this reason, the portable RA-130 Refractometer from KEM offers the possibility to store 10 different temperature compensation coefficients. This allows the operator to easily select the appropriate temperature compensation coefficient prior to measurement.

## What are Digital Refractometers used for?

The refractive index is a value specific to a material. It is therefore a quick and easy method for materials characterization and to check the purity of liquids.

Often the refractive index is used for concentration determinations in binary mixtures. The most popular concentration measurement by refractive index is the determination of the sugar concentration in water. There are many refractometers which directly display the results in so called Brix degrees: One degree Brix is 1 gram of sucrose in 100 grams of solution and represents the concentration of the solution as percentage by weight (% w/w). Such instruments are mainly popular in the food industry. The BX-1 portable digital Brix Meter from KEM is a very easy to use instrument for this application.

The RA-600 and RA-610 refractometers from KEM are ideally suited for concentration measurements: They have several built-in concentration scales and can store up to 100 additional concentration tables. With these instruments it is thus possible to cover a wide range of different concentration determinations by refractive index.