Hinds_M6A1

Course: PHYS204 Section: Module 6 Name: Kaitlin Hinds Instructor Name: Dr. Felix Rizvanov __________________________________________________________________________ Title : Snell’s Law: The Refraction Angle __________________________________________________________________________ Abstract : This experiment was set up to prove the Law of Refraction, also known as Snell’s Law. Using a computer program, I was able to observe how the angle of refraction changed in response to a change in the index of refraction and the angle of incidence. My results found that an increase in index of refraction would cause a decrease in the angle of refraction. In the latter part of the experiment, it was found that an increase in the angle of incidence would result in an increase in the angle of refraction. With these outcomes, I was able to conclude that Snell’s Law held true. __________________________________________________________________________ Introduction: The purpose of this lab was to observe the effects of index of refraction and angle of incidence on the angel of refraction. This experiment seeks to prove the theory of Snell’s Law, or the law of refraction. This can be seen in the following equation n 1 sinθ 1 = n 2 sinθ 2 . The report examines the response of the refracted angle when the corresponding index of refraction and the angle of incidence is changed. As the angle of incidence and index of refraction for the upper material were held constant, a change in the index of refraction for the lower material resulted in an opposite change in the angle of refraction. Later, both indices of refraction were held constant, and the angle of incidence was the changing variable. As the angle of incidence increased, the angle of refracted increased as well. The equations necessary for this experiment are: θ 2 = sin − 1 ( n 1 sin θ 1 n 2 ) Absolute Diff = ¿ θ 2 calc − θ 2 meas ∨ ¿ % Diff = ¿ θ 2 calc − θ 2 meas ∨ ¿ θ 2 calc ¿ Where n 1 represents the index of refraction for the upper material, n 2 represents the index of refraction for the lower material, θ 1 represents the angle of incidence, and θ 2 represents the angle of refraction. It was observed that an increase in index of refraction will cause a decrease in the angle of refraction, and an increase in the angle of incidence will cause an increase in the angle of refraction. Equation 1 Equation 3 Equation 2

__________________________________________________________________________ Methods: For this experiment, I used the bending light simulation from PHET Colorado to adjust the variables affecting the index of refraction. First, I turned on the laser and placed a protractor at the point where the two materials and the normal line meet. The angle of incidence was set to 50  and the index of refraction of the upper material was set to 1.00. I then varied the index of refraction for the lower material and measured the angles of refraction. For the second part, I removed the protractor. Next, I set the index of refraction for the upper material to 1.00 and the lower material to 1.425. I then varied the index of incidence and used computer’s angle measurements to measure the angles of refraction. __________________________________________________________________________

The data indicates that a change in the index of refraction results in the change of the angle of refraction. As the index of refraction increases, the angle decreases. The following graph illustrates the effect of the index of refraction on the angle of refraction. The data indicates that a downward trend of the angle of refraction as a function of the index for refraction. This is seen in both the measured values and calculated values.  1 Calculated  2 Measured  2 Absolute Difference |  2calc -  2meas | % Difference |  2calc -  2meas | /  2calc 10  7  7  0 0 20  13.89  13.9  0.01 0.00071 30  20.54  20.6  0.06 0.00292 40  26.81  26.8  0.01 0.00037 50  32.52  32.5  0.02 0.00061 60  37.43  37.4  0.03 0.00080 70  41.26  41.3  0.04 0.00096 80  43.72  43.7  0.02 0.00045 The following chart illustrates the effect of the angle of incidence on the angle of refraction. The data indicates that a change in the angle of index results in the change of the angle of refraction. As the angle of incidence increases, the angle of refraction increases. The following graph illustrates the effect of the angle of incidence on the angle of refraction.

The data indicates an increase in angle of reflection as a function of angle of incidence. The calculated and measured values followed the same line. Discussion : The experiment found that an increase of the index of refraction will cause a decrease in the angle of refraction. It was also found that an increase in the angle of incidence will also increase the angle of refraction. The results clearly indicate that the relationship between indices of refraction and ray angles are consistent with the law of refraction. These results are significant because it allows us to design optical devices such as fiber optics. Fiber optics have many different applications, including telecommunication services and connectivity. By utilizing light to transmit signals, fiber optic technology is more reliable than other options (Engineering, 2021). These results raise questions such as what are the other factors that effect refraction? What angle of refraction provides the best data transfer within a fiber optic cable? __________________________________________________________________________ Conclusion: The purpose of this lab was to test the relationship between indices of refraction, refracted angle, and incidence angle. Starting with a constant index of refraction for the upper material and angle on incidence, I varied the index of refraction for the lower material and measured the change in the refracted angle. It was found that an increase in the index of refraction would decrease the refracted angle. Next, both indices of refraction were held constant. I then adjusted the angle of incidence by 10-degree increments and observed the resulting angle of refraction. When the incident angle increased, the refracted angle did as well. These two different results proved to be consistent with Snell’s Law. __________________________________________________________________________ References: Engineering LibreTexts. (July 5, 2021). Snell’s Law. Retrieved April 17, 2022, from https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Sci ence)/Optical_Properties/Snell%27s_Law