phys 1112 8

1 Reflection/refraction - Remote Lab Theory: Law of reflection: angle of reflection is the same as the angle of incidence. 𝜃 𝑖 = 𝜃 ? = 𝜃 1 -----------(1) Snell’s law for refraction (above figure-1): ? 1 sin 𝜃 1 = ? 2 sin 𝜃 2 ------------------(2) Critical angle (above figure-2): sin(𝜃 𝑐 ) = ? 2 ? 1 , ? 1 > ? 2 ----------(3)

2 Reflection/refraction Lab This lab uses the Bending Light and Geometrical Optics simulations from PhET Interactive Simulations at University of Colorado Boulder, under the CC-BY 4.0 license. https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html https://phet.colorado.edu/sims/geometric-optics/geometric-optics_en.html Learning Goals A. Apply Snell’s law to a laser beam incident on the interface between media. B. Calculate the Critical angle. Exploration Explore the Intro screen to find some things that happen when light rays shine into water. Figure out how to test what happens when the light rays come from underwater. Compare your ideas about why things look different under water to how light rays appear to “bend”.

4 45 ±2 degrees 1 70 ±2 degrees 2 5. Increase the angle of incidence, 𝜃 𝑖 = 𝜃 1 slowly from 5 0 to 60 0 by 5 0 increment. What happens to 𝜃 ? and 𝜃 𝑟 ? Enter your comments. Record your data, units and uncertainties. 𝜃 𝑖 = 𝜃 1 𝜃 ? = 𝜃 1 𝜃 𝑟 = 𝜃 2 Comments 5 5 ±2 degrees 5 ±2 degrees 10 10 ±2 degrees 12 ±2 degrees 15 15 ±2 degrees 18 ±2 degrees 20 20 ±2 degrees 25 ±2 degrees 25 25 ±2 degrees 31 ±2 degrees 30 30 ±2 degrees 40 ±2 degrees 35 35 ±2 degrees 46 ±2 degrees 40 40 ±2 degrees 55 ±2 degrees 45 45 ±2 degrees 65 ±2 degrees 50 50 ±2 degrees 78 ±2 degrees 55 55 ±2 degrees 55 ±2 degrees 60 60 ±2 degrees 60 ±2 degrees 6. Measure and record the angle 𝜃 1 of incidence when the refracted beam is horizontal or angle of refraction 𝜃 𝑟 = 𝜃 2 = 90 ° . Try to do this very carefully as refracted ray could disappear, the refracted ray is very sensitive when you get close to this situation (see figire-2, page-1). This is the phenomenon of total internal reflection, where, 𝜃 1 = 𝜃 𝑐 critical angle (measured). Insert a snapshot for this situation showing all three rays as good as you can. 7. Calculate this angle 𝜃 1 = 𝜃 𝑐 using Snell’s law (equation 2), use only n 1 and n 2 values and 𝜃 𝑟 = 𝜃 2 = 90 ° , where 𝜃 1 = 𝜃 𝑐 critical angle (calculated). 1.00sin (90) 1.33 = 0.751 sin -1 (0.751)= 48.7 8. Can total internal reflection happen if the light is traveling from air into water? Explain. Try this situation using the simulation.

5 Total internal reflection occurs because the angle of refraction reaches a 90-degree angle before the angle of incidence reaches a 90-degree angle. The only way for the angle of refraction to be greater than the angle of incidence is for light to bend away from the normal. Since light only bends away from the normal when passing from a more dense medium into a less dense medium, then this would be a necessary condition for total internal reflection 9. Find the percent error of measured and calculated 𝜃 𝑐 values above #6 and #7. % 𝑒𝑟𝑟?𝑟 = 0.027% 10. Change Materials, n 1 medium-1 is water and n 2 medium-2 is glass. Can you obtain the total internal reflection for this case? If so what is 𝜃 𝑐 critical angle? Attach a snapshot. Critical angle = 30 ±2 degrees 11. Change Materials, n 1 medium-1 is glass and n 2 medium-2 is water. Can you obtain the total internal reflection for this case? If so what is 𝜃 𝑐 critical angle? Attach a snapshot. Critical angle = 25 ±2 degrees 12. Change Materials, n 1 medium-1 is Mystery A and n 2 medium-2 is Air. Can you obtain the total internal reflection for this case? If so what is 𝜃 𝑐 critical angle? Attach a snapshot. Critical angle = 65 ±2 degrees 13. Use (equation 3), Critical angle, 𝜃 𝑐 and n 2 (#12) to determine refractive index of n for the Mystery A material using recorded data in #12.