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

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

11. Lumped Circuit Schematic

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.