Refractive index as an easy inline concentration measurement.
The principle of using the refraction of light to calculate the concentration of a solution is not new; in fact, it goes back to ancient times, although not in our corner of the world. We had to wait until 1621, when Dutch astronomer Snellius rediscovered and published the mathematics behind this phenomenon.
Measuring the refractive index of light is basically measuring the speed of light in different media. In a vacuum, the speed of light, c, is a known and constant value. In any other medium, the speed of light is lower. The refractive index, n, indicates how much the speed of light in a particular medium slows down.
Where v = speed of light in the medium being studied.
The speed of light in a medium and corresponding refractive index depends on temperature and wavelength. The refractive index is therefore measured with monochromatic light with a wavelength of 589 nm at 20 °C or 25 °C. Using the wave theory of Dutch physicist and astronomer Christiaan Huygens, you can demonstrate that the angle of refraction of the light rays meets:
If we increase the angle of incidence, α, the angle of refraction, β, will also increase. At a certain angle of incidence, the angle of refraction will reach 90º, meaning the refracted light beam β will run parallel to the surface between the media.
This angle is called the critical angle.
This critical angle is exactly what is measured by a refractometer, the device for measuring the refractive index.
In a refractometer, the light beam is sent through a prism whose refractive index is precisely known. The prism is in contact with the medium whose concentration we want to calculate. The critical angle can be determined from the choice of material, geometry, the properties of the prism, and the light source. Depending on the concentration of the medium, the critical angle and thus the amount of light that is completely refracted and not transmitted into the medium varies. This ‘reflected’ light is captured by a CCD camera, and creates the optical image.
The location on the CCD camera where light is no longer detected is called the borderline. This position depends purely on the critical angle, so it makes calculating the refractive index simple.
As we have seen, the refractive index of a solution and its concentration are linked. The refractive index also depends on the chemical composition of the liquid of course, but as a rule of thumb, you may assume that each 1% difference in concentration changes the refractive index by 0.002. Temperature also plays a role. This is automatically compensated, but a difference of 0.0001 in the refractive index corresponds to a temperature difference of approximately 1 °C for aqueous solutions. Converted to concentration difference, a delta of 1 °C means a difference in concentration of 0.05%, so compensating for temperature is clearly necessary. In reality, the influence of temperature and concentration on the refractive index is unfortunately not linear, so more complicated formulas are necessary for precise calculations. The software uses polynomial functions to calculate the exact compensation.
Measuring the refractive index with a refractometer is an extremely suitable method for inline determination of the concentration of a fluid in an industrial process. Since these devices have sophisticated structures, high-quality electronics and no moving parts, they require little or no maintenance, and no regular calibration.
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