The Partial Polarization of Light by Sucrose Molecules


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The Partial Polarization of Light by Sucrose Molecules
Alexia Caldwell and Jonathan Griffey Department of Physics and Astronomy
The University of Georgia, Athens, Georgia 30602
(Dated: December 5, 2016)
The goal of this final project is to demonstrate the optical activity of chiral sucrose molecules and how they have the ability to partially polarize light. To do so we designed a device consisting of a 3D printed apparatus and a smart phone to observe the change in intensity of a light source before and after passing through a sucrose solution of known concentration. Our device will include a rotatable polarizer, a fixed polarizer, a fixed LED light source, a sucrose solution and a CCD camera to capture images of the beam after passing through all of the components. After performing an experiment in which we found the specific rotation of the sucrose solution at two different concentrations, we find that the data that we captured using our device was extremely reliable and that we were very successful in displaying the optical activity of sucrose molecules using our device.

I. INTRODUCTION
The purpose of this final project is to allow us to quantify the degree of polarization performed by a sucrose solution on light from an LED light bulb. Because we know that sucrose is a chiral molecule, we know that it has the ability to partially polarize light. We also know that the degree to which the polarization occurs is proportional to the concentration of the solution.
We used this knowledge to construct a device to be used in conjunction with a smart phone’s CCD camera, to display this principle. To do this we 3D printed an apparatus to hold a series of components and affix them to the CCD camera of an iPhone 6. These components included a white LED light, a fixed polarizer, a cuvette to hold the sucrose solution, a sucrose solution with a known concentration, a rotational polarizer and the CCD camera on the iPhone.
After constructing the device we used it to confirm that the sucrose solution was a polarizer by measuring the intensity of the light and using this data to determine the degree of polarization of the light.
II. PROJECT PRINCIPLES AND PROCEDURE
The general optics principle that we aimed to demonstrate was the polarization property of light. Specifically we aimed to show that a chiral, or optically active, molecule had the power to circularly polarize light. Molecules are considered to be optically active when the mirror images of the molecule cannot be superimposed on top of one another. Due to the fact that they are not identical twins, but rather act more like a left and right hand. Each of the two types of molecules interacts with light differently. These molecules either slow down the counter clockwise or the clockwise components the polarization, thus making one component that is not slowed

take control over the other. In this way the molecules create a plane polarized beam that has been rotated when compared to the original beam.
It is possible to quantitatively analyze this property by collecting data about the angle of polarization and the concentration of the sucrose solution. To do this we first passed a beam of LED light through a fixed polarizer, then it passed through a blank cuvette and finally passed through a rotatable polarizer before going into the CCD camera. We then determined the angle of the rotatable polarizer which minimized the intensity of the beam. Next we used a pipet to fill the cuvette with the sucrose solution. We followed the same procedure above and used the rotatable polarizer to again minimize the intensity of the beam. From this we were then able to observe that the angle which the intensity was minimized was different from the control test.
In order to measure the angles at which the intensity had been minimized we took measurements on how far the rotating piece traveled past its initial position and then used that to find the arc length. From there it is very simple to use the arc length and equate it to the angle traveled through trigonometry.
From this data we were then able to use equation (1), as shown below, to find the constant, [α]. This constant is the specific rotation of the solution and is set for each type of molecule.
(1) In this equation, α is the difference in angle between tests containing a sucrose solution and those without the solution, [α] is the specific rotation of the solution, l is the distance the light travels through the solution, and c is the concentration of the solution measured in grams of sucrose per milliliter of total solution.

III. DESIGN, PRODUCTION, AND COST
The goal of our 3D printed design was to create a housing to hold all of the components in line with the CCD camera. The entire housing is a tube of approximately eight inches that attaches to the camera on one end and on the other has a LED flash light held up by a support leg.
Starting from the light source, we chose a small LED flashlight to be taped into the end of our device to serve as the light source for the experiment. We did so because LED light is a relatively stable source of light that was also very cost effective to obtain. We spent around six dollars on the flashlight.
The flashlight fits into a 3D printed hollow cube shape and is immediately followed by the next part, the fixed polarizer. The fixed polarizer is simply a piece of a polarizer sheet that has been fastened between the two pieces of the 3D printed device, shown in figure one. The polarizer sheet was ordered off Amazon and came in a pack of multiple sheets, one used here in this part, one in the rotatable polarizer and the last fastened to the flashlight to dampen the beam. The pack of polarizers cost us ten dollars.

FIG. 2. The rotational polarizer mount. The polarizer sheet glued onto one of the thick circular pieces and the thin ring is glued to the back of that to allow us to spin the piece. Then it is slid into the end of the piece with the large hole. And the spokes are then fastened on the other side in its slots.
Finally after the rotatable polarizer, the end piece, figure three, is attached to the back on the IPhone’s camera which is used to capture images of the light beam.

FIG.1. the 3D rendering of the pieces of the device that would hold the flashlight the fixed polarizer and had the slot to hold the cuvette. The smaller piece is placed upright and the polarizer sheet is glued between it and the larger piece.
Past the fixed polarizer we placed a 10.4mm by 10.4mm square slot in the 3D printed piece to hold the cuvette, figure one. The cuvette was loaned to us by the physics lab and likely cost around ten cents. This piece is extremely important because this is what will hold our sucrose solution.
The most complicated piece of our design was the rotatable polarizer segment figure two. In order to create a piece that rotated freely we made a system of spokes that will hold a spinning piece in the base. Three spokes come out of the large circular piece of the design and are attached to the other slide into slots on the other end. Before fastening the two sides of the spokes together we will slip a circular piece that will hold the polarizing sheet into the large hole in the piece without spokes. This circular piece consists of one 3D printed pieces with the polarizer sheet glued on the end.

FIG.3. a close up view of the attachment that will fit to the back of the IPhone CCD camera via the large ring.
The production of the device took several tries over multiple weeks to finally get a design that would work the way we expected it too. The rotating piece was especially troublesome with respect to getting the scale of the pieces to fit together just right.
IV. CALIBRATION
In order to calibrate the device we took several measurements of the light intensity over several minutes with the rotational polarizer in the vertical position. This was we could know how the fluctuations in the beam would affect how our design functioned and the accuracy of the data we were able to collect.
To find the standard deviation we looked at the average standard deviation of the saturation of the pixels. We know that as the light intensity changes the saturation of the pixels will also change in a proportional manner.
Once this test was performed, we looked at the average standard deviation of the intensity over time. This value was ±47 saturated pixels for the red channel, ±59 saturated pixels for the green channel and ±70 saturated pixels for the blue light. When this standard deviation is compared to the total number of saturated pixels in each image, which was well over one hundred thousand, we conclude that they are statistically insignificant and had little effect on the results of our lab. LED light served as an especially stable light source and made our task simpler.

V. DATA ANALYSIS
Once we collected the photographs of the beam coming through the apparatus, as shown in figure four below, we then isolated only the pixels that went through the cuvette. In this way we were able to avoid interference from outside light sources and the reflection off of the red pieces of the device itself and the stack of books we set the device on.

FIG. 4. The unprocessed photo of the LED light coming through the device.
The first step to doing so is to separate the image into three different color channels, red, blue and green so as to remove excess light anomalies. We then added a pixel mask to each image, in order to isolate only the fully saturated pixels, shown below in figure five below.

FIG. 6. The isolated group of pixels that passed through the cuvette and were resulting from the LED light source.
We processed all of the images in this manner. The result was the pixel saturation on the image throughout the region that our light source passed through. We are able to use this data as the light intensity due to the fact that we know that the light source was solely responsible for the illumination of the pixels in this region.
We then plotted graphs of the intensity of the beam measured in pixel saturation vs. angle of rotation measured in degrees for the control set of data with no sucrose solution and the two sets of data collected from the tests with sucrose solution. We were able to get the most cohesive results from the green channel of light. We believe that the red and blue channels are more unreliable because the polarizer’s extinction rate for blue light is very high and the device itself is red which would have possibly skewed our data. The three green channel graphs are shown below.

FIG. 5. An example of a blue color channel pixel mask. Here only the fully saturated pixels are isolated.
After adding the pixel mask, we then isolated only the section of the data that was passed through the cuvette by isolating the large grouping of pixels that are clustered together in the center of the image. The result of the process is shown below in figure 6.

FIG.7. the intensity vs. angle graph for the control sample with no sucrose solution in the cuvette. Note that the minimum value shown on the graph is at approximately 50 degrees.

FIG. 8. The intensity of the beam vs the angle of the polarizer graph with a 0.25g/ml sucrose solution in the cuvette. Note that the minimum on the graph is at 41.5 degrees.
FIG. 9. The intensity of the beam vs the angle of the polarizer graph with a 0.2g/ml sucrose solution in the cuvette. Note that the minimum on the graph is at 30 degrees.
From the three graphs we can determine the absolute minimum intensity of the light in each of these situations. While we do not have smooth curves to pull data off of we are able to see that there is a clear point on each graph that is lower than all of the others.
From these graphs we can easily see that the sucrose solution did in fact change the degree of polarization of the light. In the control test the angle of the polarizer that minimized the intensity was 56.5±1 degrees and in the sucrose solutions we found that the angle that minimized the intensity was 42±1 degrees for the 0.25 g/ml solution and 30±1 degrees for the 0.2 g/ml solution. Not only did we see that the angle of polarization is changed, we also saw that it was changed in a way that was concentration dependent.
The deviation of ±1 on the degree values is due to the way that we measured the angle the polarizer was moving through. Because our measurement system was only accurate to the one half degree that only allowed us to be certain of our measurements to the full degree mark.
We were able to test the accuracy of our data by finding the specific rotation of the solution at each concentration. To do so we used equation one, the known concentration and the angle at minimum intensity and solved for the constant, [α]. We found that the constant value was 16±1 degrees*L/mm*g for the 0.25 g/ml solution and 15±1 degrees*L/mm*g for the 0.2 g/ml solution. From the theory we expected the values to be that same and found that the two values could be

considered statistically equivalent due to our uncertainty in the degree values used to determine these values.
VI. SUMMARY AND CONCLUSIONS
We find that we were extremely successful in creating a 3D printed device that allowed us to display the optical activity of the chiral molecule, sucrose. Our device was able measure the intensity of light at various angles of polarization with and without sucrose solution present. The device itself was very cost effective and the LED light source was very easy to calibrate because of the negligible fluctuations in intensity over time.
Once we found the angle required to minimize the intensity in each test we compared these values to find that there was polarization occurring due to the presence of the sucrose molecules. The rotation of the polarizer needed to minimize the intensity decreased by approximately ten degrees with the addition of the 0.25g/ml sucrose solution and twenty with the addition of the 0.2g/ml sucrose solution.
After displaying the fact that polarization had occurred we were able to show the accuracy of our results by calculating the value of the specific rotation of the solution of the two sucrose concentration trials and comparing those values. We found that the two values could be considered statistically equivalent due to our calculation of possible error in finding the minimum angle.
If this experiment were to be repeated and modified we recommend that the rotating piece be made larger so that it is possible to take smaller angle measurements. As it was, we were only able to measure in approximately 5 degree increments and had we been able to capture smaller measurements our data would have been more convincing. Also, we would have also liked to be able to keep the ambient light levels in the room more stable. While our method of analyzing cut out much of the excess light in the room, we still believe that fluctuations in said light may have affected our data. Our final recommendation is that distilled water should be used next time instead of plain tap water. While we do not believe that there was any other optically active molecules in the tap water, it is possible that contamination could have occurred.

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The Partial Polarization of Light by Sucrose Molecules