Lab 10 Geometric Optics PHY 112

PHY 112 3/24/2024 Geometric Optics Lab Lab Purpose/Question: The purpose of this lab is to examine the process of refraction and to experimentally be able to determine the index of refraction of water using Snell’s Law. Materials: From the lab kit, we will need a refraction cell and a laser pointer. Other materials we will need are water, protractor, ruler or straight edge, paper, and pen. Procedures: 1. Fill the refraction cell with water. 2. Trace the bottom of the cell on the sheet of paper and draw out a line every 10 degrees. 3. Point the laser pointer at the water in the refraction cell. Make sure to trace and record the index and refraction angle of the laser beam. 4. Change the incident angle of the laser 10 degrees and repeat for six trials. 5. Use Snell’s Law to find the value of N 2 by substituting the known angles and index of refraction of air into the equation and using N 1 = 1. 6. Repeat this for each of the trials. 7. Compare the accepted values of the index of refraction of water to our results. 8. Calculate the percent error of each trial. Photographs of Experiment: Data:

Trials Index of Refraction (air) Angle of Incidence (degrees) Sin (angle of incidence) Angle of refraction (degrees) Sin (angle of refraction) Index of refraction 1 1 10 0.174 8 0.122 1.426 2 1 20 0.342 15 0.259 1.320 3 1 30 0.500 22 0.375 1.333 4 1 40 0.643 29 0.485 1.326 5 1 50 0.766 32 0.530 1.445 6 1 60 0.866 40 0.643 1.347 Average = 1.366 Calculations and Graphs: - To find individual index of refraction: - Snell’s Law: N 1 sin(theta 1 ) = N 2 sin(theta 2 ) N air sin(theta) incident = N water sin(theta) refraction (1)sin(10) = N water sin(8) N water = 1.426 - Average index of refraction (1.426+1.320+1.333+1.326+1.445+1.347) / (6) = 1.366 - The refractive index of water for visible light is 1.33 - To calculate the percent error: - % error = |(#experimental - #actual)/(#actual)| x 100 % error = |(1.366 - 1.33)/(1.33)| x 100 % error = 2.71%

incidence remains constant and is equal to the ratio of the phase velocities of the two mediums through which the wave is traveling. The percentage error from my experiment was 2.71% which shows that my results were accurate. The percent difference I got for this experiment is 9.04% which is not the best but still pretty low. I think this percent difference would still be considered consistent and precise as it is not a really high number. Before I actually started the experiment, I thought the laser light would be very visible through the refraction cell. I could see the light through it but it was not as visible as I thought it would be. The thickness of the laser light was also bigger than I thought so I had to really estimate when it came to the angle of refraction. These two challenges could have caused both an increase or decrease in our measurement values. Analysis Questions: 1. If I used a very large angle of incidence it would result in a smaller angle of refraction due to the higher refractive index of water compared to air. As the angle of incidence increases, we observe a decrease in refraction and an increase in reflection, especially as it approaches a 90-degree angle. As the angle of incidence gets close to or exceeds the critical angle, there will be less refraction and more reflection due to total internal reflection. 2. A critical angle is the maximum incident angle that will allow refraction to still occur. To find the critical angle, we will use Snell’s Law: - N 1 sin(theta 1 ) = N 2 sin(theta 2 ) → N 1 sin(theta crit ) = N 2 sin(90) sin(theta crit ) = N 2 /N 1 sin(theta crit ) = 1/1.366 Theta crit = 47.06 degrees

References: - Admin. (2023, March 27). What is Refractive Index - Refractive index of water, examples and formula. BYJUS. https://byjus.com/physics/refractive-index/ - Urone, P. P., & Hinrichs, R. (2012, June 21). 25.3 The Law of Refraction - College Physics | OpenStax. https://openstax.org/books/college-physics/pages/25-3-the-law-of- refraction