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## Introduction: Gatorade's Index of Refraction

Gatorade, you drink it all the time. But have you nerds ever wondered what its index of refraction is? Well, with this amazing experiment, you will be able to find out! So fasten your seatbelts, and lets get going!

## Step 1: Gather Your Materials

Things you will need:
• Water, this will serve as the standard
• Light source
• Container for Gatorade, preferably a clear semicircular one
• Protractor
• Track to stabilize materials
• Slit plate and mask, this will focus the light to make it easier to see the angles

## Step 2: Setting Up the Experiment

To start out, place the track on a smooth level surface. This will ensure that the Gatorade stays stable in the container and that the light goes through the container completely. Place the light source on one end of the track so that it faces the opposite end. Afterwards, place the slit mask and the plate together about 10cm away from the light source. This will focus the light into a line so that you can see where it hits the Gatorade and how it refracts. Put the protractor about 20 cm away from the light source and place the container on top of it. If you have a semicircular container, you should point the round side towards the light source to make it easier to read the angle at which the light refracts.

After you are done, you should have something similar to the picture above.

## Step 3: Finding the Angle

Pour WATER into the container. Water is our standard, something to check that our experiment is going according to plan.

Turn on the light and adjust the protractor so that the light hits the container parallel to the normal axis (the bold line in the picture above). If the light is difficult to see, you may need to turn off the lights. If you have set up the experiment properly, the light should focus into a line and exit the container at an angle. In the picture above, you can see that the light bends to one side after it passes through the water.

If your protractor reads 0 degrees at the normal, then the angle of refraction can be found by looking at where the light is on the protractor. However, if it does not, then you can find the angle of refraction by calculating the difference between the angle marked by the light and 90 degrees.

Now, rotate the protractor (with the container on top) ten degrees at a time. At each interval of ten degrees, record the angle obtained, and rotate to the next angle. At the angle where the refracted light is no longer visible, or is perpendicular to the normal. Another way to check is if beyond this angle, you achieve total internal reflection. Record this angle as the critical angle. Continue beyond this point up until you reach 90 degrees, still going by 10 degree intervals.

After this, empty your container, and fill it with your gatorade. Repeat the experiment and note the critical angle. It may be different!

## Step 4: Calculating Index of Refraction

Using Snell's Law, we can determine the indices of refraction of the Gatorade and the water. n1 is the unknown, and represents the index of refraction of the desired medium. θ1 is the initial angle where the light has not yet passed through the medium. n2 is the index of refraction of air, which is equal to 1. θ2 is the refracted angle. For both the Gatorade and the water, solve the equation for n1 for every measurement, and then take the average of all the indices of refraction to come up with a final value. Also, make sure that  your calculator is in degrees!

Example:
Initial angle = 20, Refracted angle = 30
n1*sin(θ1) = n2*sin(θ2)
n1*sin(20) = 1*sin(30)
n1*0.343 = 1*0.5
n1 = 1.458

## Step 5: Our Data

(Initial angle, refracted angle)

Water:
0, 0
10, 15
20, 28.5
30, 43
40, 60
50, critical angle
60, 120
70, 110
80, 100
90, 90

0, 1
10, 14
20, 28
30, 42
40, 60
50, critical angle
60, 112
70, 110
80, 100
90, 90

Here we see that the data is slightly different, yet not very much so. This indicates that the gatorade is very similar to water, thus perhaps containing a large percentage of water.

## Step 6: Conclusion

After reviewing the refracted angles between the Gatorade and the water, we noticed that the measurements were almost the same. Although there are slight differences between the two media for some measurements, this can be attributed to the insignificant error of misread measurements. We conclude that the indices of refraction of Gatorade and water are the same. We can attribute this to the fact that Gatorade is made up mostly of water, and that the other added ingredients do not greatly affect its index of refraction.

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