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
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
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
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.