Mara Anderson / Stony Brook Laser Teaching Center

# A Systematic Investigation of Optical Activity in Sugar Solutions

## Introduction

Starting in my freshman year of high school, I had two job aspirations: become a professional dancer and then one day retire and teach math. Along the way to fulfilling those goals I took my first physics class and decided that teaching physics was by far the more interesting choice, seeing as how the student gets a hands-on real-world experience with the math.

Teaching optics in high school is always difficult. In mechanics labs students get to see hands-on demonstrations where pieces move and objects crash into each other. In electronics there are colorful wires and devices that cause bulbs to light up, or sounds to go off. There just are not as many bells and whistles involved in demonstrating the properties of light waves. In this simple classroom experiment involving linear polarizers and corn syrup, a bright and colorful display catches attention and teaches a number of valuable lessons from how a polarizer works to what makes the colors our eyes detect.

Elliptically polarized light occurs when the x and y components of the electric field vector change over time. This can lead to two special cases: if the components change over time but with the same phase, linearly polarized light is created; if the components are 90degrees out of phase, circularly polarized light is created.

## Chirality

Chirality is a property of molecules that can only be easily observed when linearly polarized light is used. Chiral molecules can have a handedness to their structure; one can be a mirror image of another but with the carbon bonds arranged differently. This difference in structure will cause light passing through the molecule to be rotated.

## Optical Activity

Due to the difference in refraction index, light entering a solution will be slowed down. The fascinating aspect of chirality (for our color construction) is that the refraction index will be greater for right circularly polarized light than for left (if the molecule is left handed), causing a phase difference between the two components and thus rotating the linearly polarized light.

The angle the rotated light makes with the first polarizer is dependent on a number of factors: path length, concentration, temperature and wavelength.

$[\alpha]_{\lambda}^{T}=\frac{100\alpha}{l\times c}$

where alpha is the specific rotation, T is the room temperature in Celsius, lambda is the wavelength, l is the path length in dm, and d is the concentration in g/mL.

## Setup

We worked with fructose in order to avoid the mixed rotations of the combination of optically active molecules in corn syrup. In order to figure out the effect of concentration and path length, two setups were created and subsequently tested with a range of wavelengths.

 Laser Type λ(nm) Red HeNe 633 Yellow HeNe 594 Green DPPS 532 Blue Argon Ion 488 Violet Diode 404

In the first, path length was held constant while concentration was varied.

(A laser beam is passed through a polarizer and then recieved by a photon detector.)

This was followed by measurements at a constant concentration but variable path length:

The data produced from these experiments will appear curved instead of linear, so it as also important to account for the change in volume of the sugar-water solution. There is no listed source for calculating the increase, so we put together a simple experiment in a graduated cylinder and found a linear relation, namely: $y=.557x+50$ , where y is volume of solution and x is grams of sugar.

## Results

Combining all of these linear concentration-path-length dependent functions, we produce a graph where we can easily see the dependence on wavelength.

After several attempts, this dependence was determined to be
$[\alpha]_{\lambda}^{21}=\frac{1}{\lambda^{2}}$

The dependence we determined also happens to lie very close to later found literature values.

Similar measurements were taken with each wavelength passing through the corn syrup (at a constant path length). Although it does not give us the path length and concentration dependence, using the slope of this relation, we can finally explain the colors we see in the original demonstration. We use the Law of Malus to determine the intensity of the different wavelengths at different angles of the second polarizer.

$I=I_{0}cos^{2}(\theta_{\alpha }-\theta _{p})$

Where I is the final intensity of the wavelength, I0 is the initial intensity, θα is the angle of specific rotation and θp is the angle of the second polarizer to the first.

At 81% concentration (roughly 73g of fructose in the original 50mL of water):
 Laser Type λ Θ Red HeNe 633nm 32.9 Yellow HeNe 594 38.0 Green DPPS 532 48.1 Blue Argon Ion 488 59.2 Violet Diode 404 87.8

## Recreating the Demonstration

Calculated spectra (intensity vs. wavelength plots) for settings of the second polarizer of 0, 30, 45, 60, 90, 120, 135, 150 and 180 degrees
relative to the first polarizer. The sequence runs from left to right, top to bottom.

## Acknowledgements

 Mara Anderson Summer 2009 Home Laser Teaching Center