Measurement Of The Speed Of Light

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Measurement of The Speed of Light Paul Sherlock Supervisor: Colette McDonagh

description

Measure of the Speed of Light presentation for project for Applied Physics degree

Transcript of Measurement Of The Speed Of Light

Page 1: Measurement Of The  Speed Of Light

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.