Worksheet for polarization

Worksheet, Properties of Light PS253-Physics Lab for Engineers Name: Speed of Light, Fiber Optics Long Fiber Optic Length: 20.01 ± 0.05m Short Fiber Optic Length: 0.155 ± 0.05 1. Using the short fiber optic cable, record the oscilloscope display of the time between consecutive transmitted pulses (Δt value). This should be between 0.5-1.5μs. 1.13 us 2. Calculate the pulse frequency of the LED transmitter circuit from your information in (1). Remember this is too fast for your eye to see the individual pulses! 3. Using the cursors on the oscilloscope, record the instrument time for each fiber. This is the time between when the signal pulse is sent and received in either fiber. tshort cable = 322.0 ± 0.05ns tlong cable = 422 ± 0.5ns Subtract the time found in the short fiber test from the long fiber test, to find the actual time of flight of the photons Δt in the long fiber. This corrects for unknown circuit time delays. 4. Subtract the short fiber length from the long fiber length to find an effective length l. Remember the Δt from (4) applies to a cable equal in length to the difference of the long and short cables. 5. Compute the critical angle (θc) for the optical fiber. 6. What happens to any light in the fiber that is travelling at an angle less than the critical angle? 7. What happens to any light in the fiber that is travelling at an angle greater than the critical angle? 8. Compute the longest optical path length Δxlongest path for the light travelling through the fiber at θc. – Page 1 of 6 – Post-Lab Worksheet, Properties of Light PS253-Physics Lab for Engineers 9. Compute the average optical path length for any light traveling through the entire fiber. 10. What is the average velocity of light inside the fiber optic cable? 11. From your results, determine an experimental value for the speed of light in a vacuum, cexp. 12. Given a precisely known reference value for c of 2.99792x108m/s, compute a percentage difference between your experimental value and the reference value. 13. Determine to what magnitude you obtained an accurate result. For example, are you accurate to 1 part per thousand (0.001) ↔ 0.1%, or 1 part per hundred (0.01) ↔ 1%, etc. 14. The speed of light is a very large number ~108m/s, and the timings involved in this experiment were very small numbers ~10-8s. However, you most likely obtained a very reasonable result considering the mathematics and physics concepts involved were relatively simplistic and straight forward. Reflect on the significance of this feat for a few moments and write your thoughts below. – Page 2 of 6 – Post-Lab Worksheet, Properties of Light PS253-Physics Lab for Engineers 15. Consider all the materials used: two lengths of fiber optic cable, two electronic circuits, a digital oscilloscope, oscilloscope probes, the LED transmitter, the photodiode detector, a ruler to measure length of the short cable, and values given to you (fiber index, long fiber length). a. Discuss what you think would be the most significant known uncertainties affecting your result? These would be uncertainties you already know exist and that you know a value for or could reasonably estimate a value for. b. Discuss what you think could be some unknown uncertainties affecting your result. These would be uncertainties you didn’t know about or did not realize existed before running the experiment and obtaining your results, or that you would not know how to estimate their magnitude. c. Out of the unknown uncertainties that you’ve contemplated above (realizing you at least know of their existence now) discuss which you think could be the most significant one impacting your result? 16. Discuss how you might improve or expand upon this experiment. – Page 3 of 6 – Post-Lab Worksheet, Properties of Light PS253-Physics Lab for Engineers Polarization of Light 17. With the polarizers positioned such that the light meter is reading near maximum intensity, yet is not saturated, record the angle of the rotating polarizer B as the zero angle reference point. Zero Angle Reference = 90 ± 0.05 18. After collecting data while adjusting the angle of the rotating polarizer B find the absolute minimum intensity. If plotting in Pasco Capstone, this would appear as the bottom of a parabola or sinusoid. Alternatively, it would be the minimum value in the datatable in Capstone. Record this minimum intensity as the background intensity point. Background Intensity = 2508 ± 0.05 Maximum Light Intensity = 5240± 0.05 19. Complete the following table for all data points collected. The first two columns should be the values collected straight from the equipment (no corrections). The remaining columns should include corrections for the zero angle offset, the background intensity subtraction, and the maximum intensity normalization (division). Relative Instrument Angle [deg] 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Instrument Light Intensity [ ] Polarizer Angle θ [deg] Normalized Light Intensity [ ] 3561.8 3317.1 3104.0 2939.3 27790 26724 2570.6 2521.9 2508.3 2529.9 2613.2 2748.3 2888.1 3064.1 3314.3 3533.2 3771.14 40342 4276.1 4528.4 4756.6 4918.4 5049.0 5234.6 – Page 4 of 6 – cos 𝜃 [radians] cos 2 𝜃 [radians] Post-Lab Worksheet, Properties of Light PS253-Physics Lab for Engineers 20. Produce two plots and include here: Normalized Intensity vs Angle θ, and Normalized Intensity vs cos 𝜃. Remember and follow the guidelines for producing good plots. Although we would not expect either plot to be linear from our background physics, include in each plot a ‘fit’ linear trendline with the equation and R2 value displayed. Consider making the fit line dashed to indicate it is only preliminary. 21. Produce one final plot and include here: Normalized Intensity vs cos2 𝜃. Follow the guidelines for producing good plots. Include in the plot a fit linear trendline with the equation and R2 value displayed. This plot should be very close to an ideal linear trend. 22. Of the three different mathematical models fit in the three plots above, which one comes closest to truly representing the behavior of non-polarized light after it is transmitted through two linearly polarizing sheets crossed at some angle θ? Note: An R2 value of 1 would be a perfect linear fit to data. 23. Do your results match what you would expect from the background physics? 24. From what you’ve learned, what would the measured light intensity be if you transmitted nonpolarized light through only a single linearly polarizing sheet? How would this intensity vary as you rotated the polarizer? Consider the initial intensity is Io. 25. If you transmit non-polarized light through two ideal linearly polarizing sheets when their polarization axes are crossed (rotated 90° to each other) what is the final transmitted intensity? – Page 5 of 6 – Post-Lab Worksheet, Properties of Light PS253-Physics Lab for Engineers 26. Starting with the situation outlined above in (26), you add a 3rd linear polarizer between the other two with its polarization axis at 45° to the first while leaving the other two unchanged. Now what is the final transmitted intensity? Consider the initial intensity is Io. 27. Discuss how you might improve or expand upon this experiment. – Page 6 of 6 –

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