Measurement Of The Speed Of Light
- 1. Measurement of The Speed of Light Paul Sherlock Supervisor: Colette McDonagh
- 2. Introduction • Important since the time of Galileo •developed down through the centuries •Frömer measured it from the rotation of Jupiter’s moon •use of Lasers (1973 - 1979) •the metre was based on the speed of light •astronomy and space travel
- 3. Experiments Standing Waves Method (Simple Approximate Methods) Lumped Circuit Method (Indirect Method) Laser Based Method (Direct method)
- 4. Standing Waves Method Principleof standing waves in a microwave oven An array of hotspots and coldspots throughout the oven’s volume Marshmallows and Fax paper c = λv
- 5. Marshmallows Method Array of marshmallows arranged on plate Put in microwave oven heated until some melted and unmelted 6 cm between unmelted (nodes) and melted (antinodes)
- 6. Marshmallows: Results using c =λv the approximate speed of light can be calculated: c = 2450 × 106 × 2(0.06m) = 2450 × 106 × 0.12m = 2.94 × 108m/s discrepancy: 5.792458 × 106 (1.9%)
- 7. Fax Paper Thermal fax paper Damp towel to absorb excess microwaves Oven turned on until burn spots (hotspots or antinodes) appeared Measured and averaged distances taken
- 8. Fax Paper
- 9. Fax Paper: results Distance λ (distance×2) Frequency (MHz) c (m/s) (m) 0.0605 0.121 2450 2.96 × 108 0.06 0.12 2450 2.94 × 108 0.066 0.132 2450 3.23 × 108 0.067 0.134 2450 3.28 × 108 0.0585 0.117 2450 2.86 × 108 0.0575 0.115 2450 2.81 × 108 0.0516 0.103 2450 2.52 × 108 0.0613 0.1206 2450 2.95 × 108 The average speed got from the experiment was 2.94 × 108 m/s with a standard deviation 2.23 × 107; discrepancy 1.6%
- 10. Lumped Circuit Method Introduction Purelyelectrical method Maxwell's Equation: c = (ε0µ0)-1/2 Long Coil Inductor Two capacitors used: Cylindrical Air Spaced Capacitor and Variable Parallel Plate Capacitor
- 12. Lumped Circuit Resonance Frequency: f = 1/2π√LC Capacitance: (Cylindrical Air Spaced Capacitor) C = (2π/ln(b/a)) ε0 (with corrections) (Variable Parallel Plate Capacitor) C =(A/d) ε0 Inductance: L = (πN2r2/l)μ0 (ε0µ0)-1/2 is found and therefore c
- 13. Lumped Circuit with Cylindrical Air Spaced Capacitor: results theoretical resonant frequency using dimensions measured: 69.31 kHz theoretical resonant frequency using the measured values: 70.7 kHz average resonant frequency determined from circuit was 68.85 kHz 68.85 × 103 = 1/2π√(5.97714302×103μ0)(79.349101546ε0) 68.85 × 103 = 1/2π√(4.74280928×105 ε0μ0) 68.85 × 103 = 1/4.32710764×103√ε0μ0 1/√ε0μ0 = 2.97921361 × 108 m/s discrepancy: 1.87 × 106 m/s (0.62%) Error: 0.27 %
- 14. Lumped Circuit with Variable Parallel Plate Capacitor: results distance Theoretical Theoretical Actual c (m/s) between resonant frequency frequency plates frequency using using dimensions measured measured values 10cm 1.28 × 106Hz 7.7 × 105Hz 16 × 106 Hz 3.74645105 × 109 5 cm 9.05 × 105Hz 6.3 × 105Hz 15.8 × 106 Hz 5.23205336 × 109 2 cm 5.72 × 105Hz 4.58 × 105Hz 15.7 × 106 Hz 8.22024449 × 109 1 cm 4.04 × 105Hz 2.2 × 105Hz 15.5 × 106 Hz 1.14770898 ×1010
- 15. Laser Based Method Introduction initial aim to measure c was to use a high frequency modulated laser beam at about 95 MHz collimated output beam transmitted to a retroflector which returns it to a photodiode detector close to the laser. Moving the retroflector along a track parallel to the light beam, the phase of the modulation in the detector current relative to the signal which drives the diode would be shifted couldn’t modulate at such high frequencies, a fast oscilloscope was employed and c was calculated from the time difference on the oscilloscope corresponding to moving the photodiode a certain distance.
- 16. Laser Based Method Setup Helium-Neon Laser acousto-optic deflector- modulator photodiode (BPX65) connected to circuit Two distances:163.5 cm and 73.5 cm
- 17. Laser Based Method Circuits
- 18. Laser Based Method sinusoidal waves
- 19. Results (2 points) Distance 1: 163.5 cm Distance 2:73.5 cm Phase Difference 352 ns 348 ns 4 ns 226 ns 220 ns 6 ns Using c = distance/phase difference Distance Phase Difference c (m/s) 0.89m 4 ns 2.225×108 0.89m 6 ns 1.483×108
- 20. Results using Easyplot More accurate phase difference using all points of the whole waveforms Distance 1: Distance 2: (163.5 cm) (74.5 cm) 5.7 ns 3.14 ns c = 1.635 − 0.745m/5.7ns − 3.14ns = 0.89m/2.56 × 10−9s = 3.47 × 108m/s discrepancy: 4.7207542 × 107
- 21. Conclusion The purpose of this project was to try and accurately measure the speed of light a number of different ways. From the simple experiments using marshmallows and fax paper to the more accurate indirect, purely electrical (LC Circuit) and direct (Laser-based) methods. The LC Circuit method proves that light is an electromagnetic wave from Maxwell’s theory c = (ε0μ0)−1/2 The direct, Laser-based method proves that light can be measured in a lab at reasonable distances rather than terrestrial distances using the equation: speed = distance/time The most accurate method used was the LC method with the Cylindrical Air Spaced Capacitor because it was within 0.6% of the established speed with a relatively low experimental error (0.27%). The Laser Method experiment could have been an accurate experiment but there was limitations that could not be solved to achieve the high frequency that was required.