Dependent – r (radius of colorless ring)
Controlled – temperature; strength of laser; distance between laser and bottom of cup; (concentration of sugar – in the “water + sugar” version of the experiment)
Materials:
A small white cup with a flat, matt bottom; plotting paper of accuracy 2 mm; red laser pointer; tripod; mineral water “Kropla Beskidu”; white sugar; retractable flexible rule (accuracy 1 mm)
Methods:
The experiment was conducted at minimal light required to make observations. Excessive light would cause the rings (which are the essence of the experiment) to become blurry, thus prohibiting proper data collection.
First of all we marked a point on the plotting paper – this would be the center from which we would measure our radii. Then we attached this paper to the bottom of the cup, so that the point we marked was at the place of the real center of the vessel. Having the cup ready, we fastened the laser pointer to the tripod, which would free our hands and enable us to write down our observations immediately. What is important, we had to connect both items in way that we would be able to have the pointer working for a longer period of time, without our action (most pointers work only when their button is pressed and hold – we have to arrange everything, so that we remove this necessity – the complete setup is shown in fig. 2). Now we may move on to the proper experiment.
We filled the cup with water to about 1 cm (pouring too much will result in the rings being excessively large, making precise observations impossible.) Next, we had to measure the exact depth of water, using the retractable flexible rule. Once this was done, we moved the filled cup to our second construction, and we positioned it so that the laser beam pointed at the center we marked earlier.
Once we activated the laser pointer, we should have seen two rings being formed on the surface of the water - an inner, colorless ring, and a larger red ring. What we did now was, we measured (using the plotting paper) the radius of the smaller, colorless ring. Once the data was collected for the first trial, we removed the cup from the construction (which we turned off to preserve battery life), and we repeated the experiment without changing the depth of water.
We repeated these methods (including making two trials for each depth) at different water depths, though we remembered that at high depths we would not notice the rings.
The second experiment was to be carried analogically, with the difference of using the same mineral water, but saturated with white sugar. In order to create a saturated solution, we mildly heated the water in a separate vessel and added small amounts of sugar, mixing constantly. At the point, where no more sugar dissolved in our mixture, we stated that the solution was saturated. We then waited for it to cool down to room temperature, after which we decantated it over the excess sugar to another vessel. The experiment was then conducted using this mixture, instead of plain water, according to earlier guidelines. The measurement uncertainties in both versions of the experiment were taken as the smallest division of scale (1 mm for the retractable flexible rule and 2 mm for the plotting paper, respectively.)
Data obtained in the experiment:
For Mineral Water:
For Mineral Water + Sugar:
Calculation:
To calculate the refractive index (here nliquid), we start with the formula:
In order to calculate αcritical we use the equation:
Merging both formulae, we get the expression:
From which we are able to calculate the refractive indexes of our selected liquids using the data collected. The uncertainty of nliquid was calculated through the equation:
The results of our calculations:
For Mineral Water:
For Mineral Water + Sugar:
Evaluation:
As our results show, our hypothesis (which was a test of the reliability of our method), that the mixture of water and sugar will have a higher refractive index than plain mineral water, was, indeed, correct. This gives us strong belief, that the refractive index of water, as calculated by us, is correct also, thus proving that the method we used is viable. Indeed, the officially accepted refractive index for pure water (in the experiment we used mineral water, which may have a bit larger refractive index) is 1.33, which is a quantity that lies in our [1.32;1.56] range of possible values.
The data accuracy could be improved, with the use of a more precise measuring device, instead of the plotting paper. Using a stronger laser beam could increase the intensity of the red ring, making the change of color sharper, thus also improving accuracy of the data. Using pure water could have, of course, also lowered the difference between our results and those widely accepted.
If we consider the different physical features of both plain water and our mixture, we may notice a connection between a fluid’s viscosity and it’s refractive index. It will be greater for thicker liquids like our mixture and smaller for thinner liquids such as plain water. With density it is analogical – plain water (which has a lower density value) will have a lower refractive index.
Conclusion:
Though the exact results of our experiment differ slightly from those proved using more sophisticated methods, the accuracy of our data is acceptable. We proved the efficiency of the critical angle method at estimating the refractive index of a liquid. Furthermore, we proved our hypothesis that a saturated mixture of water and sugar will have a greater refractive index than plain water, which is a fact very important for industry, because it may serve as the basis for a method of analyzing and separating plain water and its solutions.
Experiment conducted by:
Krzysztof Kaczmarek
Krzysztof Koc
Lab Report written by:
Krzysztof Kaczmarek
References:
http://www.szczecinek.gawex.pl/icspdsi/pliki/wyznaczanie.pdf
http://en.wikipedia.org
http://chemistry.about.com
http://www.translate.pl
