Download - Measurement Of The Speed Of Light
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Measurement of The Speed of Light
Paul SherlockSupervisor: Colette McDonagh
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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
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ExperimentsStanding Waves Method (Simple Approximate Methods)
Lumped Circuit Method (Indirect Method)
Laser Based Method (Direct method)
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Standing Waves MethodPrinciple of standing waves
in a microwave ovenAn array of hotspots and
coldspots throughout the oven’s volume
Marshmallows and Fax paper
c = λv
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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)
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Marshmallows: Results
usingc =λv
the approximate speed of light can be calculated:
c = 2450 × 106 × 2(0.06m)= 2450 × 106 × 0.12m
= 2.94 × 108m/sdiscrepancy: 5.792458 × 106 (1.9%)
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Fax PaperThermal fax paperDamp towel to absorb excess
microwavesOven turned on until burn
spots (hotspots or antinodes) appeared
Measured and averaged distances taken
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Fax Paper
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Fax Paper: results
The average speed got from the experiment was 2.94 × 108 m/s with a standard deviation 2.23 × 107; discrepancy 1.6%
Distance(m)
λ (distance×2) Frequency (MHz) c (m/s)
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
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Lumped Circuit Method Introduction
Purely electrical method Maxwell's Equation: c =
(ε0µ0)-1/2 Long Coil Inductor Two capacitors used:
Cylindrical Air Spaced Capacitor and Variable Parallel Plate Capacitor
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Lumped Circuit Schematic
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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
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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 %
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Lumped Circuit with Variable Parallel Plate Capacitor: results
distance between
plates
Theoretical resonant frequency
using dimensions measured
Theoretical frequency
using measured
values
Actual frequency
c (m/s)
10cm 1.28 × 106Hz 7.7 × 105Hz 16 × 106 Hz 3.74645105 × 109
5 cm 9.05 × 105Hz 6.3 × 105Hz 15.8 × 106
Hz5.23205336 ×
109
2 cm 5.72 × 105Hz 4.58 × 105Hz
15.7 × 106
Hz8.22024449 ×
109
1 cm 4.04 × 105Hz 2.2 × 105Hz 15.5 × 106
Hz1.14770898
×1010
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Laser Based MethodIntroduction
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.
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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
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Laser Based Method Circuits
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Laser Based Methodsinusoidal waves
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Results (2 points)
Using c = distance/phase difference
Distance 1: 163.5 cm Distance 2:73.5 cm Phase Difference
352 ns226 ns
348 ns220 ns
4 ns6 ns
Distance Phase Difference c (m/s)
0.89m0.89m
4 ns6 ns
2.225×108
1.483×108
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Results using EasyplotMore accurate phase difference using all points of the whole
waveforms
c = 1.635 − 0.745m/5.7ns − 3.14ns =
0.89m/2.56 × 10−9s
= 3.47 × 108m/s
discrepancy: 4.7207542 × 107
Distance 1: (163.5 cm)
Distance 2: (74.5 cm)
5.7 ns 3.14 ns
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Conclusion The purpose of this project was to try and accurately measure the speed of light anumber of different ways. From the simple experiments using marshmallows andfax paper to the more accurate indirect, purely electrical (LC Circuit) and direct
(Laser-based) methods. The LC Circuit method proves that light is an electromagneticwave 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 ratherthan terrestrial distances using the equation:
speed = distance/time
The most accurate method used was the LC method with the Cylindrical AirSpaced Capacitor because it was within 0.6% of the established speed with a relatively
low experimental error (0.27%). The Laser Method experiment could havebeen an accurate experiment but there was limitations that could not be solved to
achieve the high frequency that was required.