APH04_Snell's Law (1)

Old Dominion University Physics 112N, Online Lab 1 OLD DOMINION UNIVERSITY PHYS 112 – Asynchronous Online APH04 – SNELL’S LAW Submitted By: 1. Kiley Ligon 2. Amari Bangurah 3. Submitted on Date

2 Experiment APH04: Snell’s Law Snell’s Law Experiment APH04 Objective Describe what happens to light when it shines on a medium Explain light direction changes at the interface between two media and what determines the angle Apply Snell’s law to a laser beam incident on the interface between media Determine the angle of total internal reflection at the interface between two media Materials Computer with internet access Theory Snell’s Law The direction of light propagation changes abruptly when light encounters a reflective surface. The direction also changes abruptly when light passes across a boundary between two different media of propagation, such as between air and acrylic, or between glass and water. In this case, the change of direction is called Refraction. As for reflection, a simple law characterizes the behavior of a reflected ray of light: θ incident = θ reflected (1) Where the incident angle is equal to the reflected angle. According to the Law of Refraction , also known as Snell’s Law : n 1 sin θ 1 = n 2 sin θ 2 (2) where the quantities n 1 and n 2 are constants, called indices of refraction , that depend on the two media through which the light is passing. An index of refraction is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. For the most common materials, this value is usually greater than 1. A table summarizing the indices of refraction for common materials is found below. Materia l Index of Refraction Vaccum 1.000 Air 1.0003 Water 1.333 Diamon d 2.42 The angles θ 1 and θ 2 are the angles that the incident and refracted rays make with the normal to the boundary between the two media. The normal is defined by being perpendicular to where the plane

4 Experiment APH04: Snell’s Law What do you notice about the brush at the boundary from the air to water? The handle appears to be to the left of where the head of the brush is. Try this at home with some other things like a spoon or fork. Do you observe anything different? (If you don’t have a clear glass, you can still see some interesting things. You might need to a larger container like a bathroom sink to get a view from a lower angle). I was able to achieve similar results by similar means. What ideas do you have about why things look different under water? Explain what is happening at the air/water boundary to cause the object to look broken. It is an optical illusion that light plays with our eyes. As light hits the water, it is refracted, as it hits the object placed in the water it is reflected back at us. For the rest of this experiment, we will be using a PhET simulation to observe and prove Snell’s Law. Visit the website: https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html Explore the Intro screen to find some things that happen when light rays shine into water. Use both the Ray and Wave models for light. Describe the behavior of light when it transitions through the boundary from air to water. (A video titled Refraction in the Lab Manual folder may be useful for this question.) Use the following relevant vocabulary words in your summary: index of refraction, incident angle, reflected angle, and refracted angle. As the laser comes in at larger angles compared to the normal, is the light refracted more or less than when it comes in at angles closer to the normal. Look at the intensity of light that is reflected vs. refracted as the angle changes. When is more light reflected (higher or lower angles with respect to the normal)? When is more light refracted? Part B: Snell’s Law Move to the More Tools screen to test Snell’s Law.

Old Dominion University Physics 112N, Online Lab 5 Set up your simulation so that the laser shines from air into glass. Change the laser’s wavelength (color) to 632nm. This is the wavelength of the very popular HeNe (helium-neon) laser. (The wavelength of this type of laser is 632.8nm but the simulation can’t do fractional wavelengths.) Drag the protractor to the middle of the simulation, and align its center with the normal of the glass (the vertical, dashed line) and where the laser makes contact. Review Data Table 1, and for each incident angle given, measure the refracted angle of the laser. If you are unable to get the exact angles from the data table, that’s fine. Get values that are close and then update the data table with your new incident angles. Continue filling in Data Table 1 by calculating the sine of the incident and refracted angles. We have provided a spreadsheet titled APH04 – Snell’s Law.xlsx which make make it easier to perform the calculations more quickly. Excel requires angles be recorded in radians! This conversion is quick in Excel. We won’t give away the process since it’s fairly straightforward and you’ve been practicing with spreadsheets for several experiments now. If we take take Snell’s Law and solve for sin θ 1 we find sin θ 1 = n 2 n 1 sin θ 2 Using your data in Data Table 1, create a graph of sin θ 1 vs. sin θ 2 . (This will plot the sine of the incident angle on the y-axis and the sine of the refraction angle on the x-axis.) Add a linear trendline to the data, display the equation on the chart, and include the graph in your lab report.

Old Dominion University Physics 112N, Online Lab 7 Data Table – Experiment APH04 Data Table 1 Snell’s Law Index of Refraction of Air (n 1 ) 1.000 Index of Refraction of Glass (n 2 ) 1.501 Incident Angle θ 1 Refractio n Angle θ 2 Sine of Indiciden t Angle Sine of Refractio n Angle 0° 0 0 0 10° 6.6 0.174 0.115 20° 13.2 0.342 0.228 30° 19.5 0.5 0.334 40° 25.4 0.643 0.429 50° 30.7 0.766 0.511 60° 35.3 0.866 0.578 70° 38.8 0.94 0.627 80° 41 0.985 0.656

8 Experiment APH04: Snell’s Law Data Table 2 Mystery Material A Incident Angle θ 1 Refractio n Angle θ 2 Sine of Incident Angle Sine of Refractio n Angle 0° 0 0 0 10° 4.1 0.174 0.071 20° 8.1 0.342 0.141 30° 11.9 0.5 0.206 40° 15.4 0.643 0.266 50° 18.4 0.766 0.316 60° 21 0.866 0.358 70° 22.9 0.94 0.389 80° 24 0.985 0.407

10 Experiment APH04: Snell’s Law Data Table 4 Mystery Materials Index of Refraction of Mystery Material A Index of Refraction of Mystery Material B 2.420(Diamond) 1.401(??)

Old Dominion University Physics 112N, Online Lab 11 What to Turn In  Full Lab Report  Data Tables 1-4  Graph of sin θ 1 Questions to Consider When graphing sin θ 1 vs. sin θ 2 , what shape does the data take in this graph? Discuss any trends you see. The graph appears to take a logarithmic shape as it narrows in on 90°. When graphing sin θ 1 vs. sin θ 2 , what does the slope of the data represent? What value is the slope similar to? Given Snell’s Law, what do you expect for the slope? Discuss. The slope seems to plateau after it gets closer to 90°. Thoroughly explain what you did to determine each material’s index of refraction, how you did it, and then report your value of n for both materials in Data Table 4. For fiber optic cables, which use light to transmit data, the idea is to shine light through a cable such that much of the light is reflected internally and makes its way to the other end of the cable. In a fiber optic cable, would you want a steeper or more shallow angle for which total internal reflection occurs? Explain. (Keep in mind that a “shallow angle” in this case is a smaller angle with respect to the normal of the boundary.) Acknowledgements Portions of this experiment were designed by Trish Loeblein at the University of Colorado Boulder.