Physics 4C Chabot College Scott Hildreth

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1 Physics 4C Chabot College Scott Hildreth Snell s Law with Microwave Optics Experiment Goals: Experimentally verify Snell s Law holds for microwaves. Lab Safety Note! Although the microwaves in this experiment are not inherently dangerous, they can cause water to evaporate, and consequently they should never be aimed at the eyes. They are generated by a klystron tube, which also will heat up during the experiment. Be careful not to touch it. A. Exploring Reflection 1. Set up the system with a flat metal reflecting plate (a microwave mirror ) at the central point, and vary the incoming incident light from the transmitter between 20 to 70 degrees. Rotating the receiver on the goniometer, measure and record the angle of reflection - and your uncertainty where the receiver intensity is maximized. Receiver Microwave Mirror Angle of incidence Angle of refraction Figure B1 testing reflection; varying incident angles Transmitter Reflected Angle Reflected Angle

2 Additional questions to answer for part A: 2. Does the angle of incidence appear to be the same as the angle of reflection? How certain are you given the uncertainties in measurement in this lab? 3. Note in your data for reflection where the incident and maximum intensity reflected angles do not seem to be the same. What might be causing this result? What could you do to minimize the effect? 4. Ideally this experiment would be performed using the incoming light as a plane wave. Is it? How would the departure from a plane wave affect this particular experiment? B. Exploring Refraction 1. Set up the system with the arms of the goniometer initially 180 degrees apart, parallel to the long side of the lab tables. Place the empty semi-circular Styrofoam (acting as a microwave lens ) at the central point, so that the incident light falls on the CURVED side of the container. The flat side of the container should be exactly at the rotation axis. (Figure C1) Figure B1 testing refraction; incident angle of 0 degrees Transmitter Receiver 2. In one more step, you ll fill the empty container with polystyrene beads, and determine their index of refraction for microwave radiation. But good experimental technique involves ensuring that the container alone doesn t interfere with your results. Design a short experiment to determine whether the Styrofoam container alone refracts the microwaves. Describe what you did, and your results. 3. Now fill the container with polystyrene beads. Vary the incoming incident light from the transmitter between 0 and 70 degrees. Being careful to ensure that you are measuring the proper angles, rotate both the transmitter and the receiver on the goniometer, and then measure and record the angles of incidence and refraction - and your uncertainty where the receiver intensity is maximized.

3 Angle of incidence Figure B2 testing refraction; varying incident angles Receiver Transmitter Angle of refraction Refraction data: Polystyrene beads 1 Refracted Angle 2 n1 = sin ( 2 ) / sin ( 1 ) Refracted Angle 2 n1 = sin ( 2 ) / sin ( 1 ) Additional questions to answer for part B: 4. From your data, using Snell s law, n 1 sin ( 1 ) = n 2 sin ( 2 ), find (n2), the average value of the index of refraction for the polystyrene beads for this wavelength of microwaves. Here, n 2 will be 1 (meaning that the speed of light in air is almost as big as it is in a vacuum). so: n polystyrene = sin ( 2 ) / sin ( 1 ) 5. What is the uncertainty in your measurement of n polystyrene? 6. Do you believe your results will change if, rather than using small beads, you used a solid block of polystyrene? Why? Report requirements: Each student should submit ONE abbreviated report, mentioning all participants names and including copies of the data sheets from both this experiment and the Inverse Square Law (Intensity of Light vs. Distance) experiment performed in the prior week. Include ONLY the abstract, the data tables, and the answers to the questions in both labs. Don t take time recopying data tables. The abstract will be most important of this abbreviated report

4 Physics 4C Chabot College Scott Hildreth Snell s Law with PhET Bending Light Simulation* (1) Start the PHeT simulation entitled Bending Light. The simulation is available at the PhET website: (2) Start with the Intro box, explore the simulation s capabilities. Turn on the laser and drag the circular protractor such that the protractor is centered along the normal line and the boundary between the two mediums. Pull out the intensity meter and note how you can measure the relative intensities of refracted (transmitted) and reflected beams. Vary the materials both above and below the interface. Explore which material (Air,, Glass,, or ) produces the largest amount of reflection compared to transmission. (3) Determine the experimental values for the indices of refraction for both materials and using Snell s Law. Make a small data table, varying incident angles and recording the resulting refracted angles. How precise can you measure angles? Calculate n for each observation, and determine the average n for the each material. It will be your choice as to how many observations you need. Consider what would make your simulated experiment more precise! Average n A = Average n B =

5 (4) Click on the More Tools box. Make sure to select Ray and check the Angles box. Turn on the laser and again drag the circular protractor such that the protractor is centered along the normal line and the boundary between the two mediums. Also, drag the speed indicator tool out from the tools located at the lower left corner of the simulation. (5) The index of refraction, given by the letter n, is defined as the ratio of the speed of light in a vacuum to the speed of light in a medium: n = c/v, where c = 3 x 10 8 m/s. Use the speed tool to measure the velocity of light in the glass, and verify that n(glass) = c/v(glass). (6) Now repeat your earlier experiment with the two Mystery materials, and use the Speed Tool to determine the speed of light in that material, and verify the actual indices of refraction n = c/v match your experimental values determined with Snell s Law. Actual n A = c/v A = Actual n B = c/v B = (7) Change the simulation to have water at the top, and air at the bottom. Find the critical angle for total internal reflection for this combination, and verify that angle satisfies Snell s Law. Repeat for the other following combinations of materials: Light coming from Glass Glass Light moving into Air Air Glass Measured Critical Angle Critical Angle from Snell s Law Difference

6 (8) Now use the PRISMS Box, and explore how the shape of a prism affects the refraction angles of the light. You can use and rotate the protractor, and turn in the Normal line, to help you estimate angles of incidence and refraction. (9) Select the circular prism, and water as the object, select the Reflections option, and investigate how rainbows both primary and secondary are created. Develop your own experiment to measure the angular dispersion of colors from a spherical drop, and record any appropriate data. Can you quantitatively determine the difference in n for violet vs. red light? If so, with what precision? If not, why not? This is a TEAM activity. Please turn in just ONE data sheet with the names of all participants. * Adapted 10/2017 from Discovering Snell s Law by Jonathan Carlson, PhET Contributor,