# Kool As Light!

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In this science experiment we will be finding the speed of light through different flavors of Kool-Aid!

Why you may ask? In this lab you will explore one method for finding the index of refraction of any material, and the the speed of light inside of that material! As the lab progresses you will learn what refraction is and how to use Snell's law!

Kool-Aid was simply the "material" we chose to use for this lab, and can be replaced with another if the methodology is altered slightly.

## Step 1: Explanation of Concepts.

This experiment revolves around Snell’s law (n(i) sin θ (i) = n(r) sin θ (r)), where the incident angle,  θ(i), is proportional to the refraction angle, θ(r). The n represents the index of refraction, which measures the density of the optical material, and can be found using the equation n = c/v, with c being the speed of light in a vacuum* and v being the speed of light in the material. The v changes at it enters or exits a material; as a result, you will have a n(i) and a n(r). In this experiment n(i) = air = 1. We know the incident angles and we will measure the refraction angles. All we have to solve for is n(r) using Snell’s law and then solve for the speed of light using n = c/v. We can then figure out the index of refraction and the unique speed of light through Kool-Aid. Sounds pretty cool, huh?

* c = 299 792 458 m / s

## Step 2: Gather Your Materials.

Here is what you will need.

•  A laser
•  Kool-Aid flavors (which flavors is up to you! We used grape, cherry, lemonade, orange, and ice blue raspberry lemonade - YUM)
•  Sugar (optional)
•  A 2 liter pitcher
•  A semi-circular dish
•  A 360° protractor

If you don't have a 360° protractor lying around you can print this one or find another one to print online.

## Step 3: Prepare the Kool-Aid.

This should be relatively simple. Follow the instructions on each Kool-Aid flavoring packet. Add sugar if you desire. In fact, you may want to make two batches of Kool-Aid, one with sugar and one without!

## Step 4: Set Up Your Experiment.

The picture on this step should help you set up if you are having trouble understanding the following directions.

•  The laser should be set up so it points directly into the center of the flat side of the semi-circular dish.
•  Under the semi-circular dish, place your 360° protractor so that the laser enters above 0° and exits above 180°. Also, make sure that the flat side of your semi-circular dish is lined up along a line which connects 90° and 270°.

## Step 5: Take Your Data!

Now comes the fun part! You get to observe refraction at work!

Here is a data sheet to help you along with your collection process (the only columns you will need for now are the “Angle of Refraction” columns).

1.  Pour your selected flavor into the semi-circular dish to a level where the laser will pass through it.
2.  Place the filled semi-circular dish into the correct position as shown during the setup step.
3.  Find the angle of refraction at each of the following incident angles*, 15°, 30°, 45°, 60°, and 75°, and record each angle on the data sheet (if you are confused study the diagram; if you are using our 360° protractor you will need to do some simple subtraction or addition to find the correct angle).
4.  Repeat steps 1 through 3 for each of your flavors.

* the angle of incidence is the angle at which the laser enters the flat side of your semi-circular disk

## Step 6: Analyze the Data.

If you've been confused as to why you have done a few of the things in previous steps, now is where you begin to understand! Look at the different line graphs for each of the different flavors. They look awfully similar, don’t they? For each incident angle that you used to measure the refraction angle, there is a unique association as displayed on the graph.In this case, the greater the incident angle, the greater the refraction angle. For example, for the cherry graph, as the incident angle increased from 0 to 75 degrees, the refraction angle increased similarly from 0 to 44 degrees, creating a linear association. Looking at the figure with the line graphs of all the flavors, it is clear that they are very similar as the line graphs almost blend in with one another. However, the red line indicating the association between incident and refracting angles for the cherry flavor is slightly different than that of the other flavors. At an incident angle of 30 degrees, the refraction angle is 18 degrees, much lower than that of the other flavors. Additionally, the incident angle of 60 degrees led to a refraction angle  42 degrees instead of 40 degrees that measured in the other flavors. It is also notable that the slope of the line graphs decreases slightly from 60 to 75 degrees, almost as if the linear pattern begins to level out horizontally.

## Step 7: And Finally, in Conclusion...

After the analysis of our data, it appears that despite the different flavors of Kool-Aid used in the experiment, the refraction angles for each independently applied incident angle are relatively similar. It is also evident that human error may play a role throughout the data collection process. As the incident angle increased, the beam which was refracted widened; as a result, it was difficult to determine a precise refraction angle. This may account for the leveling out of the slope of the line between the incident angles of 60 to 75 degrees. Consequently, in future experiments, it is advised to limit the range of the incident angles to at most 50 degrees. All in all, it is safe to conclude that there is no significant difference in the indices of refraction for the different Kool-Aid flavors, thus no difference between the speeds of light of each flavor. This is not surprising as the only major difference between the flavors are the food dye whereas the rest of the ingredients are fairly similar.

In this specific experiment, we did not add sugar to our kool-aid, but it would be interesting to find out whether the concentration of sugar in the Kool-Aid has a substantial effect on the refraction angles. A higher sugar concentration may lead to a higher or lower index of refraction. Who knows? It’s up to you to find out! You can repeat this experiment, but this time, be sure to make standards for the different concentrations of sugar and begin measuring the refraction angles for each flavor.