# Finding the Index of Refraction of Hair Gel

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In this experiment, we hoped to apply our knowledge in hopes of successfully finding the index of refraction of and speed of light in hair gel.

For this experiment, we will need:

Hair Gel (Translucent or Transparent)
Straight baseboard
A tilted base with attachable, circular protractor (or similar set up)
Light source
Slit mask
Slit panel
Semi-circular dish (image shown is with sample)

Explanation of Principles:
The reason that a simple white light source was used is because the hair gel in our experiment was light blue, which indicates that the blue wavelength would be the only light to pass through our medium and we did not have access to blue light. Additionally, it was not a single straight line, beam, but a long narrow beam so that we would be able to easily determine the angle of incidence at the same time the light passed through the material. A semicircular dish was chosen as the shape of the vessel for the hair gel because of the optical properties it would provide. First, it had a clear, straight edge which the light beam could strike, making it easy to control the angle of incidence. Then, after passing through the hair gel, the light would always exit perpendicular the surface of the plastic, based on the laws of geometry, which means that the light would not refract upon exiting, thus allowing us to easily measure the angle of refraction.

Snell’s law tells us that n1sini=n2sinr. Here, we know that n1= 1 because it is air, and we know the angle of incidence and angle of refraction (i and rrespectively)  based on the measurements taken during the experiment. Thus, it is an easy matter to find the index of refraction of the hair gel using the data and the trendline made from the data.

The index of refraction is also given by the equation n = c/v, where c is the speed of light (2.99792458 x 108 m/s, or for our purposes, 3 x 108 m/s) and v is the speed of light in our material. Thus, using our calculated index of refraction, we can find the speed of light in our material by the equation v = (3 x 108 m/s) / n.

Results:
Index of Refraction: n = 1.36
Speed of Light = 220,588,235 m/s

The above were created using the slope of the trendline of Excel (based on all the data we gathered) for the index of refraction.

Sample Calculation of Index of Refraction:
n = sini/sinr
n = sin(30)/sin(22)
n = .5/.374607 = 1.33

Sample Calculation of Speed of Light:
v = c/n
v = (3 x 108 m/s)/1.33
v = 225,563,910 m/s

Conclusion

This experiment may have a couple sources of error. The first instance may come from the air bubbles that were trapped in the hair gel because of its high viscosity. The light passing through the hair gel could have also passed through these bubbles, which may have caused some bending of the light. Therefore, it would be beneficial if next time, all the air bubbles could be removed prior to experimentation, though this might be hard because of the highly viscous nature of hair gel. Additionally, it appears that not all of the light refracted at the same points, since at times, the ray of light was dispersed over several angles, the highest of which was measured. This was most likely due to the air bubbles that were in the hair gel, which again, should be removed prior to experimentation.

However, this experiment did an overall good job on helping to explore methods in calculating the index of refraction of a material. It helped to reinforce the information on refraction in a medium and how how light behaves. While there was room for improvement in the design of the project, it did well for what it was.

## Step 1: Setting Up -- the Base, Protractor, and Light

Set up long, straight baseboard to help align all items and place light source at one end of the platform. Then place a slanted surface (protractor base), so that it slants toward the light source. Set the protractor on the protractor base, and letting it be secured in place. Use a slit mask and slit plate (or other appropriate tools) to create a single, vertical beam of light that passes straight across the plate

## Step 2: Setting Up -- the Sample

Fill a clear plastic semi-circular dish with hair gel. Place the dish so that the flat side is perpendicular to the light source (Angle of refraction = 0). Turn the light source on and rotate the protractor ten degrees clockwise. Note the angle of light refracted by reading the resulting angle from the protractor, and compare this to the angle of light refracted when the protractor is rotated ten degrees counter-clockwise. These two angles should be equal. If they are not, adjust the alignment of the sample until the angles match.

For best results, turn off the lights! It is much easier to see the beam of light in the dark.

## Step 3: Data Collection

To collect data, rotate the protractor base back to its original position (angle of incidence = 0), and then rotate the base so that the angle of incidence is 10 degrees in either direction. Record the angle of refraction.
Repeat for each angle increment of 10 from 20-80 degrees.

## Step 4: Data Analysis

Calculate the sine of each angle of refraction and incidence. Plot the calculated values with Sin(Angle of refraction) on the horizontal axis and Sin(angle of incidence) on the vertical axis.
Then find the slope of the line of best fit. This is your index of refraction of the medium.
Divide the speed of light (3 x 10^ 8) by your calculated index of refraction, which will result in the speed of light in the medium.