Today’s post will be relatively short but I was eager to share with you the early results of my last experiment. As the title suggests, it is about the measurement of refraction in thin films of liquids. More precisely, it is about the measurement of the refractive index of the liquid.
There are several definitions on what is refractive index depending on which side you are (experimental or theoretical physics). Basically, the refractive index is the measure of how much lights rays are slowed down in a medium when compared to travelling in vacuum. An effect of this slowing down motion is that rays which do not fall perpendicular on a surface will have their direction changed through a process known as refraction and which is best illustrated with the famous Snell’s-Descartes relation:
which says that a light ray coming from a medium of index n1 and hitting a second medium of index n2 with an angle θ1 will be bended to the output angle θ2 at the interface between the two media.
Refraction occurs everywhere in optics and is the reason why lenses act as lenses but here we will focus on the fact that, like many other parameters, refraction indices can be used to evaluate the composition of liquids. Each liquid, being pure, a mix or a solution, will have a given refraction index. Tracking the refraction index of a solution when its constituents are known can help to quantify the proportion of these constituents into the mix. This is typically how the amount of sugar is evaluated in grape juice.
A photography of the experimental setup is shown in Figure 1. It was not optimized yet but the results are already very promising despites its relative simplicity.
The instrument is composed of a right angle prism, two lenses, a 626 nm red LED light source of 18 nm FWHM, a 220 grit diffuser, a ~2 mm iris, a photodiode and some driving electronics (see below). Everything is held together using Thorlabs cage system, two post holder and a custom prism holder part that you may download at the end of the post to reproduce by 3D printing. I paid less than 20€ for the model at [∞] Materialise.
A schematic view of the setup is shown in Figure 2. The schematic also includes a neutral density filter whose role will be detailed later.
Although the setup uses a prism, it is not designed on the conventional Abbe refractometer but instead uses the critical angle of the prism to evaluate the refraction index of the liquid sample.
The idea is to generate a spot of a few millimetres diameter on the prism surface such that it comprises many different ray angles. This is done using the LED source with the coarse diffuser and the iris that is imaged by the relay lens group. The diffuser is used to artificially increases the LED light rays angle beyond the original LED emission cone. The lenses are simply two short focal lengths plano-convex lenses used as a relay imaging system.
At the interface prism/liquid, lights rays will experience refraction and enter the liquid. The output angle will be, according to Snell’s-Descartes law:
with θ1 the angle of the light ray before it refracts, θ2 the angle of the light ray after it refracted, n1 the refractive index of the prism and n2 the refractive index of the liquid.
Since most glasses usually have higher refractive indices than liquids, n1/n2 > 1 and there exists angles θ1 such that the refraction becomes non-physical because it would imply that sin(θ2) becomes greater than unity. When such condition is met, refraction does not occur and light is simply reflected on the surface. We then talk about total internal reflection. The angle at which this phenomenon starts to occur is called the critical angle and is equal to
For N-BK7 glass (n=1.50) and water (n=1.33), the critical angle is about 69.4°. It means that only light rays hitting the surface of the prism with angles lower than 69.4° will refract, all other rays being reflected at the interface.
This is precisely how the instrument identifies the refractive index of the liquid. This is because the LED/diffuser generates light rays in all directions before it hits the surface of the prism (tilted by 45°). Some light rays will refract into the liquid and some others will be reflected because they have too large angles. The instrument then gathers all the reflected light rays and re-image them on the photodetector. If we change the liquid, the refraction index will be slightly different and another amount of light rays will reach the detector. By measuring the received energy on the photodiode, we therefore have a direct relation with the refraction index of the liquid being measured.
Let us now discuss the role of the neutral density filter.
At first, I tried the experiment without the neutral density filter by simply measuring from a droplet put on the surface of the prism. This gave inconsistent results with liquids that had different wetting properties. For instance, it was working well with water but gave completely erroneous results with alcohols (I tested both methyl and ethyl alcohols). This is because the droplet becomes very thin on the surface of the prism (it wets the prism very well) and we end up with an alcohol/air interface that also has its own critical angle. However, the critical angle of that new interface is this time much less than for the prism/liquid interface and it reflects a lot of energy back to the photodiode such that we do not measure the prism/liquid interface anymore but the liquid/air interface this time.
There are two solutions to that problem. Either you work with a thick-enough liquid, for instance by placing the prism in your reaction vessel, or you place a neutral density filter on top of the liquid. I have chosen the latter here but the former is completely valid; it just applies to different experimental configuration. The neutral density filter is best suited when you manually take a drop of liquid and sandwich it between the prism and the neutral density filter. The drop will be elongated to a very thin film which is sufficient for evaluation.
The overall idea is that light rays that have refracted into the liquid should be dissipated by some means so that they never re-enter the prism. With the thick-liquid solution, they just get dissipated in the bulk phase of the liquid. With the neutral density filter, they are absorbed by the glass. To be effective, the neutral density filter should be typically OD3 to be sure that no light reflects on its back surface (glass/air interface). Also, the glass should have a refractive index lower than the one of the prism otherelse you will measure the reflection on the liquid/filter interface.
This is about everything for the theory. In practice, it does not require much more understanding except on how we extract the signal.
If we just turn the LED on and read the photodiode, we will end up with both the reflected light of the prism/liquid interface but also with all the stray (ambient) light that made its way up to the detector. If we try to make accurate measurement, it is therefore not an optimal solution.
Instead, we may modulate the LED with a square wave signal at about 1 kHz and send the output of the photodiode to a [»] bandpass filter. This way, we remove all the contribution of ambient light (which rarely fluctuates at more than 100 Hz) and only keep the signal of the LED. By measuring the peak-to-peak (or RMS or whatever you prefer) of the AC signal, we will get our measurement. In practice, I did that simply using my oscilloscope by setting the channel to “AC” mode and by setting the measurement to RMS mode. Later, it is better to have dedicated electronics for that.
The results are presented on Figure 3 for four different solvents. I also added the best fit line between the point to evaluate the early performance of the system.
Even if there are only four measurement points, the trend is linear in the studied range as could have been expected. Each liquid is clearly identifiable and the resolution of the instrument was evaluated using 95% confidence intervals to 0.0014 units of refractive index. This is already very nice knowing that it is hard to do much better than that without thermal control because organic liquids typically have temperature sensitivity about 0.0001-0.001/°C.
Obviously, with only four data points it is a bit difficult to conclude yet on the performance but this is very promising considering the simplicity of the instrument. I will try to make an updated version in the following months to complete on that.
You can download the CAD of the prism holder [∞] here. It requires two 1.5D M4 helicoils and was designed to be used with Thorlabs P911 right angle prism. You can insert 6 mm rods of Thorlabs cage system on the side to do like on Figure 1 but it requires some gentle force so be careful.
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