Sugar Pie Honey Bun, You Know That I Refract You!

(The effect of varying sugar solution concentrations on the index of refraction)

By: Haley Rott, Cindy Lara, and Salam Masalmeh

Introduction.:.

Refraction is the change in direction of the propagation of a wave due to its change in transition medium ("Shoaling, Refraction, and Diffraction of Waves."). Due to the change in medium the the phase velocity of the wave changes, but the frequency remains constant (Ward). Refraction is described by Snell’s Law which states that for a given medium, and a wave with a single frequency, the ratio of the angle of incidence  θ1 and the angle of refraction θ2 is equivalent to the ratio of phase velocities (v1 / v2) (Sommerville). In general the incident wave is partially refracted , and partially reflected (."Refraction of Light: As It Passes from Less Dense to More Dense Mediums”).

Refraction can be seen when looking into a bowl of water ("Shoaling, Refraction, and Diffraction of Waves."). Air has a refractive index of 1.003, and water has a refractive index of 1.330. If a person looks at straight object, such as a pencil, it appears to bend at the water’s surface ("Refraction of Light."). Due to the fact that the light rays are being bended as they move from the water to the air (Ward). Once the rays reach the eye, it traces it them back as lines of sight (Sommerville). This causes the water to appear shallower and the pencil to appear higher up than it actually is ("Refraction of Light."). The angle of refraction in water is especially important to take into consideration for spear fisherman because their target will appear to be in a different place. So, they must aim lower to catch the fish (Sommerville).

Method

Materials Needed:

Prism, sugar, scale, laser, ruler, string, water, and a graduated cylinder

Procedure:

The first thing you do is get your sugar solutions ready. We did 10 different percent variations (0, 5, 10, 20, 30, 40, 50, 60, 70, and 80). To make the 10% sugar solution you mix 10 grams of sugar with 90 ml of water and for 20% sugar solution you mix 20 grams of sugar and 80 ml of water. You then repeat these steps for the rest.

After your sugar solutions are prepared, you can then begin the refraction of light. The first step is to place a sheet of large paper on a flat wall. After that you place a laser on top of an item that is approximately 1-2 inches high (I used 2 coasters) and shine it at the wall making sure the laser is secured to the surface it is on so it won’t move. You then place the prism on a piece of paper on the surface (not the elevated one) approximately 1-2 inches in front of the laser (between the laser and the wall) and trace the prism in order to make sure the prism remains in the same place. With the prism empty you shine the laser through the prism and mark on the paper where it hits the wall. Label this point B. Then you mark where the laser enters the prism on the paper below it (label it point E) and where it exits the prism (point E). Remove the prism and draw a straight line from D to E. Fill the prism up with water and place it back on the spot. Rotate the prism so that the laser line going through the prism is parallel with the base side of the prism that has no laser through it. Record where the laser hits the wall and label it point A. Mark on the paper below the prism where the laser exits the prism and label it point F. Remove the prism and taking a string, place it on point A on the wall and pull it to where it hits point F and crosses the D to E line. Label this point C. Measure the distance from point A to point B (this is x), and measure the distance from point B to point C (this is L). Using X and L, do atan (X/L). That answer is θmd. Using the equation n = 2.00056 sin (0.5(θmd +60°)) solve for n (the index of refraction). Repeat these steps for your other variations Data: Data Files: text .:. Excel Conclusion:

Our results show that the higher the sugar concentration, the higher the refraction index. It also shows that the refraction index increases at a positive slope.

Our hypothesis is accepted because we said the higher the sugar concentration, the higher the refraction index and this is what happened. We can see this by 0% sugar having a refraction of 1.36 and 8-% having a refraction of 1.49. We also said it would be a positive slope with the refraction index on the y axis and the sugar solution on the x axis. This is also how the data turned out being that the r-squared value is 0.98. Therefore, our hypothesis is correct and is accepted.

The data turned out the way it did because as more sugar is put into a solution the solution becomes denser. Refraction is when light passes from a less dense solution to a denser and when the light passes through, the density change makes the light bend. In this experiment, as more sugar was added, the density of the solution increased therefore making the light bend more and producing a greater index of refraction. This was especially prevalent when the 70% and 80% sugar solutions were used because the solutions were so thick and dense that they were almost like glue. This makes sense because they were becoming denser by the large amounts of sugar and therefore bending light more.

One of the sources of error was the method of getting the liquid in and out of the prism. The prism was small so liquid was hard to get in and out. A syringe was used to get the liquid in but it caused a lot of air bubbles to also make their way into the prism and the solution. Also, when trying the get the solution out, it was impossible to get every last drop out so this could’ve potentially impacted the results.

Another source of error was the prism. It was very small so it was hard to see where the exit points were and was hard to get accurate measurements in such tight quarters.

Lastly, the laser could’ve been a source of error. The laser’s width of light was average but in this experiment it was a little too large and caused some uncertainty as to where to mark the laser hitting and where to measure from.

One solution is to buy a large prism. This would solve getting the solutions in and out and would also help with the accuracy of the data and allow more space to make accurate measurements.

Another solution would be to find a finer point laser. This way, the point would be smaller and lead to more accurate data.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html

This link explained how to calculate the index of refraction and it also explains how the index of refraction changes as it moves from fast mediums to slow mediums.

http://www.physicsclassroom.com/class/refrn/Lesson-1/Refraction-and-Sight

This link explain the broken pencil theory and why when you look at certain objects in water they are not actually where you perceive them to be.

http://www.coastal.udel.edu/ngs/waves.html

Explains how the index of refraction of a wave is affected by the depth of the water

http://ww2010.atmos.uiuc.edu/%28Gl%29/guides/mtr/opt/mch/refr/more.rxml

Visual example of index of refraction as it passes from dense to less dense mediums.

http://iopscience.iop.org/1367-2630/7/1/213

Explains origins of negative refraction.