1. Bishop 1
Measuring the Speed of Light in Air Using Modulation:
A Whole Lot to c here.
By Clayton Bishop, Richard Wang, and Henry Donaldson
Research Advisor: Dr. Melanie Lott
Department of Physics and Astronomy
Denison University, January-February 2015
Abstract
The speed of light, c, seems infinite to the naked eye. If I turn on a lamp in a dark room, I
would not expect to see photons engulfing the darkness like ocean waves on sand. The light
simply seems to appear throughout the room instantly. In fact, if I wanted to be able to truly
notice the light’s travel time (~1 second), I would need to be in a room with a length equivalent
to the distance between Earth and the moon.
Three trials were taken during the course of this experiment, with measured values of c
being (2.88 ± 0.14) E8, (2.67 ± 0.24) E8, and (3.20 ± 0.14) E8 meters/second. Comparing these
numbers to the commonly held belief that light travels at approximately 3 E8 meters/second
might make these results seem flawed. However, the calculation of these results’ weighted
average ended up being the saving grace in this experiment. If I call the set of measurements
taken to be x1, x2, and x3 and make their weights (w1, w2, and w3) equal 1/ϭi, then weighted
average equals the summation of w terms times the x terms quantity divided by the sum of w
terms. Taking w1= 5.10 E-15, w2= 1.74 E-15, and w3= 5.10 E-15, the weighted average of the
data is (2.99 ± .09) E8. This agrees within .01% with the excepted value.
2. Bishop 2
Introduction
Since what is being searched for is a velocity, a well-known and fundamental equation
can be the basis for discovery:
Velocity (m/s) = Distance (m)/Time (s)
All that it takes to figure out the speed of light is the path it travels and the time it takes to
make that trip. Until the most recent century, this was easier said than done. Due to technology
available at the time, path lengths of several kilometers had to be used just to measure the most
infinitesimal elapses of time. Today, with the aid of oscilloscopes, experiments to find the speed
of light are not as complicated and do not require as much drudgery to set up. In comparison,
modern tests require less physical labor and more technological savvy. Setting up the light’s path
would end up taking my group only about an hour of adjusting mirrors. Meanwhile, learning
how to use the different machines necessary for getting distinguishable results would take over a
month. In its most rudimentary form, the essentials of this experiment are getting a common red
light source from a powerful Helium-Neon laser, modulating the light into a waveform, splitting
the beam into two paths, sending them each a different distance into a photodetector, and
measuring time differences in between peaks of their waveforms. An accurate value for the
speed of light can be determined once the respective differences in time and distance can be
accurately measured. After that, considerations for error analysis need to be made if data analysis
proves unexpected. Potential errors could range from uncertainty in the tape measure, to “bugs”
in a function generator, to not carefully considering the differences in index of refraction
between a vacuum and the atmosphere the experiment is taking place in. The accepted speed of
light value should be within the margin of error considerations of whatever value is
experimentally demonstrated.
3. Bishop 3
Light has been studied by humanity for thousands of years. Before any experiments were
ever made, it weighed on the minds of ancient philosophers. In the 5th
century B.C., Greek
scholar Empedocles considered light using pure reason. His argument was that something is
emitted by luminous objects that is picked up by eyesight.i
Thus he was the first to theorize light
had a finite velocity.ii
Aristotle was another Greek thinker who lived shortly after the time of Empedocles. Like
his predecessor, Aristotle pondered the nature of light and whether or not its velocity was
instantaneous or finite. He theorized light did not have a velocity but rather was a medium
through which humans saw.iii
He created an interesting hypothesis; “…we should assume a time
when the sun’s ray was not as yet seen, but was still traveling in middle space.”iv
The sun began
burning approximately 5 billion years ago. If there were hypothetically a human placed on Earth
at that exact moment, she would be in darkness for 8 minutes before the sun’s first light reached
her. Aside from the numbers that are now known, this is what Aristotle speculated.
Religious texts can be important, in a spiritual sense, to specific groups of people. But it
is not often they contain complex scientific observations. This statement is untrue for a particular
measurement used in the Quran, the sacred text of Muslims. The Muslims believe that angels
travel at a finite speed, that of light.v
So using their knowledge of lunar cycles, they were able to
calculate a numeric speed of light in the 5th
century A.D. The number, 1200 lunar orbits per
Earth day, is within 0.01% precision to the speed of light from a geocentric perspective.vi
Since
the Earth is orbiting the sun and has some acceleration, they are not in the same inertial frame.
When Muslim academics made this calculation, they were unaware of the non-inertial reference
frame of the sun and the effects of its gravitational field. Since they did not account for this, their
answer has 11% error from the current accepted value.vii
4. Bishop 4
This calculation was believed by those of the Islamic faith, but was not generally
accepted by the scientific community. Thus, the speed of light was widely considered to be
infinite for the next 1200 years.viii
Finally, in 1638, famous Italian physicist Galileo Galilei
became the first to attempt to experimentally find the speed of light. He and an assistant stood at
a far, known distance apart. Each of them carried a lamp with a cover over it. Galileo also held
some sort of time-keeping device. When they were ready, the assistant removed the cloth from
his lamp and Galileo measured the amount of time it took for the light to “reach” him.
ix
Unfortunately, this was essentially only measuring the human reaction time. Galileo summed
up to the speed of light to be “extraordinarily rapid,” with his best estimate being more than ten
times faster than the speed of sound.x
Several decades passed and the speed of light still did not have an accepted numerical
value. That problem would soon be solved. In the late 17th
century, Dutch astronomer Ole
Roemer was examining the motion of Jupiter’s moons.xi
From this Roemer recognized the now
fundamental concept of gravitational force, F is proportional to 1/r2
. As distance between a moon
and Jupiter decreased, the moon’s velocity increased. He deduced that light needed extra time to
travel when Jupiter was further away, and came to the conclusion that it moved at 200,000,000
meters per second.xii
Compared to modern measurements, there is about a 33% error from this
value.
The world would have to wait until 1725 before it got a measurement within 1% of the
current accepted value. In that year, Englishman James Bradley used stellar aberration to make
an impressively accurate measurement, 301,000,000 meters per second.xiii
An aberration is
something unexpected.xiv
Stellar aberration is a ratio between the Earth’s orbital velocity and the
speed of light. Further experiments throughout the 19th
century featured rotating wheels of teeth
5. Bishop 5
with a light beam being shown through them. This is similar to my experiment in that the
vibrating flint crystals inside the AOM act like rapidly spinning teeth, chopping up the light. The
light would go hit a mirror several miles away and bounce back. By varying the frequency of the
wheel, researchers were able to determine how fast it should be rotating for light to be able to
pass back through the same gap. Scholars such as Hippolyte Fizeau and Leon Foucault used this
method of experimentation.xv
The most accurate non-modern measurement made on this topic was by Albert Michelson
in 1926. Using a known path distance of several kilometers, a series of mirrors, a rotating prism,
and a light source, Michelson was able to measure the speed of light. He did this by sending
directing the light source through the prism and over the course of several kilometers. Mirrors
sent the beam back to the prism, and by the time it had returned the prism had rotated 1/8th
of
itself.xvi
The value he derived from this experiment was 2.9974 x 108
meters per second.xvii
The
experiment itself took several years to set-up as incredibly precise path measurements were
made. Michelson reasoned that any error from his measurement was due to the 1925 Santa
Barbara earthquake changing the path distance by a couple feet.xviii
Today, the scientific community accepts the speed of light in a vacuum to be at 2.997925
x 108
meters per second.xix
So the number for light in air could possibly be less since my
experiment is taking place at 293 meters above sea level. The index of refraction for air at STP is
1.00029, so the speed of light should be corrected to 2.998794 E8 meters/second.xx
Interestingly
enough, the British and American best values are slightly different, although their margins of
error overlap.
It is my groups hope to be able to replicate this result so as to obtain a better
understanding for the constant that has been used repetitively in our studies over the last several
6. Bishop 6
years. Quantitatively, I understand c to be roughly equivalent to 3 x 108
meters per second and
useful for solving Lorentz’ transformations. If I know the wavelength of any light, I easily can
find its frequency since I know the velocity. This experiment is being done for the purpose of
qualitatively getting a better understanding of light speed and how incredibly fast something
must be moving to even be at a fraction of c, and thus experiencing time dilation/length
contraction.
Theory
Despite being extremely fast, the speed of light is still finite and thus is able to be
measured. Light itself can be defined as electromagnetic radiation or "visually perceived radiant
energy."xxi
In this experiment, light will be found using differences in time and distance. While
this is true, c can also be found with a combination of wavelength and frequency:
c (m/s)=λ (m) *f (s-1
)
Wavelength and frequency are inversely elated. The wavelength of the Helium-Neon
laser used is 633 nm. The 633 nm is significant because it falls within the visible light range of
the electromagnetic spectrum. The visible light range, from 400 nm to 700 nm, is significant
because the human eye can see it unaided. Sunlight and fluorescent light fall under this category.
The laser could have been ultraviolet or infrared, but since it is visible we can see the beam and
thus send it along any path with relative ease.
At this point in the theory behind this experiment, everything has been fairly
straightforward. But a major step has yet to be mentioned, and that is getting readable waveforms
on the oscilloscope. If the laser beam is sent directly to a photodetector, it appears as a flat line
on the scope. The more intense the light is, the higher its voltage and thus the y-value will
7. Bishop 7
change on the screen. While this is a start, it does not allow us to discern peaks/troughs necessary
for calculating time difference between the beams. Clear peaks/troughs are required so that the
cursor can be placed on a noticeable feature instead of a random place on the slope. Getting the
beams to exhibit wave-like behavior requires the combination of three machines: an Acousto-
Optic Modulator (AOM), a function generator, and a modulator. The AOM is angled slightly and
placed directly in front of the laser. The AOM's main function is to implement Bragg Diffraction
on the original beam. Bragg Diffraction splits a single beam into separate, linear beams. The
original beam remains unmodulated (m=0), but now has slightly less intense beams on either
side of it (m=1) with even less intense rays next to those (m=2) and so on. This diffraction is
caused by what lies inside the AOM. The inside of an AOM consists of flint crystals that shake
at a rapid, modulated frequency determined by an input of two function generators. The first
generator sends out a massive carrier frequency to the AOM. The second generator modulates
the carrier frequency with a smaller one, which causes irregularities in the wave and makes it
easier to read on the scope. In comparison, the different waveforms by themselves will look like:
Plot[Sin[40 ∗ 𝑡], {𝑡, 0,10}]
2 4 6 8 10
1.0
0.5
0.5
1.0
8. Bishop 8
Plot[Sin[1 ∗ 𝑡], {𝑡, 0,10}]
With the top graph representing the carrier frequency and the bottom graph showing the
modulating frequency. The modulating frequency must be on the scale of 1 MHz due to the order
of magnitude of the path distance. If it were lower, say in the 100 kHz range, the distance of the
longer beam would have to be on the scale of hundreds of meters which would cause a lot more
work and agonizing. The signal sent to the AOM is then a superposition of these two plots. It
looks like:
Plot[Sin[40 ∗ 𝑡] + Sin[1 ∗ 𝑡], {𝑡, 0,10}]
Time difference can be measured by placing one cursor on a noticeable peak in the short
distance beam's waveform, and another cursor on the long distance beam's waveform. When it is
read, it appears as a regular sine wave. On the oscilloscope, this should look like:
2 4 6 8 10
1.0
0.5
0.5
1.0
2 4 6 8 10
2
1
1
2
9. Bishop 9
This value will then be used to divide the path distance difference and result in the having
an answer for the speed of light.
Two factors need to be considered when choosing the diffracted beam that will be sent to
the splitter and become the foundation of the experiment. First, the beam must be experiencing
modulation from the flint crystals. This rules out the central beam, which will still appear as a
flat line on the scope if it is picked up by a photodetector. Secondly, the selected beam needs to
be intense enough that it can be visible during the set-up of the longer path length. The greater
the distance, the less visible a ray of light becomes. So choosing an intense beam makes
reflecting it off the series of mirrors simpler. This factor eliminates the outer rays coming out of
the AOM as they are the dimmest. The best options for the experimental beam are either m=1 or
m=2.
2 4 6 8 10
1.0
0.5
0.5
1.0
4 6 8 10 12
1.0
0.5
0.5
1.0
10. Bishop 10
Experimental Methods
Behind any successful experiment is a strong foundation. In this case, that foundation is a
sturdy, level table with a sheet of metal on top. This metal sheet has evenly spaced holes that are
advantageous for fastening down instruments with screws. It negated a large part of the
vibrations caused by the laser. A Spectra-Physics Stabilite™ Model 1248 Helium-Neon laser
rests at one end of the table. The laser is 80 centimeters long and faces the rest of the table. An
Acousto-optic modulator stands 31 centimeters away from the nose of the laser and is tilted at a
slight angle (Its function was described in the Theory section
and is thus omitted here). Attached to the AOM is an important
blue cord with a known impedance of 50 ohms. The blue cord
leads to the RF Output of the DE-40 RM Deflector Driver,
which is producing a carrier frequency of 40 MHz. The
Modulation Input on the DE-40 is then connected to the RF
Output on the monolithic HP 8656B Function Generator. The
HP produces a variable frequency that we chose to be 1 MHz and sends it back to the DE-40.
The result is a superposition between the two frequencies and now the light, after passing
through the AOM, has the potential to appear as a modulated waveform on the scope.
11. Bishop 11
A key component of this experiment is using a beam splitter. After a single beam of light
hits the splitter, it comes out in separate parts. One continues through while the other experiences
internal refraction within the glass and is reflected back towards the source at an angle. The
beam that goes through can be sent some further distance using a series of lenses and mirrors
before returning near the source. When it comes back from its trip to the main setup, it is sent
through a lens and into a photodetector. Meanwhile, the beam that is sent back at the splitter goes
through a lens and into another photodetector located less than a meter away. The two beams
have different path length and thus there is discrepancy in travel time.
After traveling through the AOM, the beam experiences Bragg Diffraction and comes out
in a ray spectra. The carrier level knob on the DE-40 can be adjusted to change the intensity of
the spectra. We maximized this since the beam would be traveling a reasonable distance and
wanted to ensure we could see it the whole time. Approximately 70 centimeters in front of the
AOM is a black card. This card’s function is to block the main beam
(m=0) and all the rays to one side of it. As a result, only three visible
rays make it to the beam splitter behind the black card. My group
decided to use the m=1 beam since it was the brightest remaining and
was being modulated in the necessary manner. Part of a black card
was placed on part of the beam splitter so that the m=2 and m=3
beams would be blocked. This setup left us with only the m=1 beam, the one we would center
our experiment on. The beam splitter is also at an angle and thus non-perpendicular to the edges
of the table.
The beam splitter sent back one beam while allowing another beam from the same source
to pass through. The beam that was reflected underwent refraction within the beam splitter. A 35
12. Bishop 12
millimeter lens is located 31.75 centimeters away from the beam splitter, back towards the
AOM. This lens focuses the light into Photodetector 1, which is 3.18 centimeters behind it. If the
light is intense enough and hitting the correct spot within the “eye”, then Photodetector 1 will
pick up a signal. This signal is sent through an attached cord and to Channel 1 of our high-tech
oscilloscope, the WaveSurfer™ 104 Xs. The connection of the cord to the scope is mediated by
the presence of a 50 ohm terminator, which reduces the noise in the signal. It also gets very hot
so caution should be used when handling.
Meanwhile, the ray that passed through the beam splitter travels out the laboratory door
and into the hallway to Mirror 1, which is 5.52 meters away. The light reflects off Mirror 1 and
heads down the long hallway for a variable distance d1 to Mirror 2.
Then, forming approximately a right angle, the light travels a short
distance d2 to Mirror 3. Mirror 3 then directs the light back down the
hallway towards the laboratory. Along the way, it passes through a 5
meter lens that my group found necessary for keeping the width of the
beam manageable. If at any point the beam got too wide and unfocused,
intensity could be lost which would increase the error in the resulting signal. After being
refocused by the lens, the beam hits Mirror 4. The variable distance between Mirror 3 and Mirror
4 has been labeled as d3. Mirror 4 reflects the light back into the laboratory and through a 35
centimeter lens, a void of 533.4 centimeters. Finally, after going through this lens, the ray travels
34.3 centimeters to Photodetector 2. Photodetector 2 is attached by cord to Channel 2 of the
WaveSurfer oscilloscope. Once again, a 50 ohm terminator is used to reduce noise in the signal.
If everything goes smoothly and the path difference between the beams is sufficient, two wave
forms that are slightly offset will appear on the scope screen. Find distinct peaks within the same
(Mirrors 4 and 1)
13. Bishop 13
wavelength to set cursors on, then observe the time difference. There was a way to reduce noise
after the effect of the terminators was in place. Setting the scope to sweep over 100 different
measurements and average the data resulted in a clearer final waveform. We set the time base (x-
axis) to 1 microsecond per division, though we could have put it on the nanoseconds scale. The
microsecond scale had more pronounced peaks thus we knew precisely where to put the cursors.
The use of lenses turned out to be technique that none of us considered using at first but
became crucial to getting the long distance beam back to the laboratory. Initially, there was no
card blocking the m=2 and m=3 beams on the splitter and we were simply ignoring them. Putting
the card there made the experiment more orderly and focused on m=1. The less beams shooting
around the room made the setup neater. Turning off a majority of the lights in the hallway made
it easier to track the path of the beam and get it aligned on the correct mirrors (Diagram of
Experimental Setup is the last page of report).
14. Bishop 14
Data Analysis and Discussion
Name of length Length (in) δ (in) Conversion
Length
(cm) δ (cm) Conversion
Length
(m) δ (m)
Laser-AOM 13.25 0 2.54 33.655 0 100 0.33655 0
AOM-Splitter 29.75 0 2.54 75.565 0 100 0.75565 0
Splitter-35 mm lens 12.5 0 2.54 31.75 0 100 0.3175 0
35 mm lens-
Photod. 1 1.25 0 2.54 3.175 0 100 0.03175 0
Splitter-Mirror 1 219 1 2.54 556.26 2.54 100 5.5626 0.025
Mirror 4-35 cm
Lens 210 1 2.54 533.4 2.54 100 5.334 0.025
35 cm Lens-
Photod. 2 13.5 0.5 2.54 34.29 1.27 100 0.3429 0.013
Trial 1 Length (in) δ (in) Conversion
Length
(cm) δ (cm) Conversion
Length
(m) δ (m)
d1 953.75 3 2.54 2422.525 7.62 100 24.22525 0.076
d2 12 0.5 2.54 30.48 1.27 100 0.3048 0.013
d3 963.83 3 2.54 2448.1282 7.62 100 24.481282 0.076
d4 964.75 3 2.54 2450.465 7.62 100 24.50465 0.076
Trial 2
d1 360 1 2.54 914.4 2.54 100 9.144 0.025
d2 22 0.5 2.54 55.88 1.27 100 0.5588 0.013
d3 370.65 1 2.54 941.451 2.54 100 9.41451 0.025
d4 370 1 2.54 939.8 2.54 100 9.398 0.025
Trial 3
d1 961.5 3 2.54 2442.21 7.62 100 24.4221 0.076
d2 397.7 2 2.54 1010.158 5.08 100 10.10158 0.051
d3 1049.8 3 2.54 2666.492 7.62 100 26.66492 0.076
d4 971.5 3 2.54 2467.61 7.62 100 24.6761 0.076
Trial #
dref (m)
δdref
(m) dsig (m) δdsig (m) Δd (m) δΔd (m)
1 0.34925 0 60.2508 0.1146 59.90158 0.1146
2 0.34925 0 30.35681 0.05327 30.00756 0.05327
3 0.34925 0 72.4281 0.1248 72.07885 0.1248
The tape measure used was marked in inches, so every measurement and its uncertainty
was converted to meters. The tape was only 30 feet long, so for longer distances it took 2-3
measurements to get a final tally. Each time we moved tape I put down some electric tape on the
floor to mark where to begin the next measurement. Each time a new one was taken on the same
15. Bishop 15
length, we added an inch of uncertainty to account for possible inaccuracies while resetting the
tape. Also the measuring tape was not stiff and so slight curves were visible in it when it
stretched out to maximum length. Another distance uncertainty came about from the 35
centimeter lens. The frame holding the lens is thick and metal, so getting an exact measurement
from the lens itself was difficult. To compensate, we added another half inch of uncertainty.
As mentioned, d1, d2, and d3 are the variable lengths we were hoping to change from
trial to trial if time permits. We chose d1 and d3 to extend the entire length of the hallway in
order to get the maximum path difference. To eliminate uncertainty, I considered the paths each
ray takes. Up until the beam splitter, both rays have the same path. At this point they split and go
their separate ways. So I eliminated the distance between the laser source and the splitter to
further reduce possible uncertainties. The punchline here is that the best measurements with
uncertainty are 59.9 ± 0.1, 30.0 ± 0.1, and 72.1 ± 0.1 meters. The fractional uncertainty is less
than 1%.
The total uncertainties for distance were calculated by adding directly. Since path length
is just the summation of different distances in an overarching path, the uncertainty in the final
measurement equals the sum of the partial uncertainties.
On the oscilloscope, our modulated waves had an evident shift, meaning the path
difference was satisfactory. Before any measurement was made, Henry set the scope to do 100
sweeps of the data in order to find an average. Then we set our cursors on an abnormal, easily
identifiable bump located on the peaks of each waveform. Also, we paid attention made sure the
cursors were not more than one wavelength from each other.
17. Bishop 17
The best measured time differences with uncertainty between peaks were, respectively:
208 ± 10, 112 ± 10, and 225 ± 10 nanoseconds. The decision to make the uncertainty 10
nanoseconds in every case is because finding an exact place to rest the cursor was a subject of
debate. A range of approximately 20 nanoseconds could be reasoned as the correct spot for the
cursor. For example, in Trial 3, Henry could have said the time difference was 217 nanoseconds
whereas Richard may have argued it was 230. I would look at both values and concurred that
either value was precise since an exact peak was difficult to locate. Ultimately, my group
concluded ± 10 nanoseconds from the most popular time difference would be used as the
uncertainty.
Once the distance and time values were calculated, it was time to solve for the speed of
light numerically. Dividing the best answer for distance by the best answer for time gave the best
measurement for the speed of light. The uncertainties were in meters per second were not quite
as simple but were still found using a theorem located in the front cover of An Introduction to
Error Analysis. The equation used to compute uncertainty is:
Ƌc= cbest*Sqrt[(Ƌx/x)2
+(Ƌt/t)2
]
Conclusion
The most difficult part of this experiment was understanding how the frequency
generators behaved and operated. This took nearly a month to completely comprehend, and once
that was done we were able to get experimental data within one lab period. Due to this, I learned
machinery is not always reliable and it is beneficial to test each piece on their own to
troubleshoot any problems. At first I was against using small-scale testing before moving on to
the actual experiment because I viewed it as a waste of time. But now from experience I can say
18. Bishop 18
that small-scale testing is imperative. This is because it takes little work and let’s one know if
everything is running smoothly. We incorporated this by only sending the “long” beam to Mirror
1 and back to see if there was a time difference. When it turned out something was wrong, I was
glad that I did not set up the entire series of mirrors.
I speculated that perhaps the reason the measured speed of light was less than the actual
value was because of the lenses our beam traveled through. Glass has a higher index of refraction
than water (~1.5 vs. 1), and so every time the beam went through a lens it briefly slowed
down.xxii
The widths of the two lenses used in the longer beam were 0.01 and .014 meters. The
width of the lens in the shorter beam was 0.035 meters. The time each beam spent in lenses can
be found by the following equation:
Tl= ((dl*nglass)/c) - ((dl*nair)/c)
Where dl is the summed width of the lenses each beam goes through. For the longer beam, the
time spent is on the order of hundredths of a nanosecond. The shorter beam experienced even
less time in the lenses, but also on the order of hundredths of a nanosecond. Since the time
differences in peaks was measured to be on the scale of hundreds of nanoseconds, the effect of
the lenses on our outcome is negligible.
I make the educated guess that the less the path difference is, the less the time difference
between peaks will be. Complimentary to that, there is a maximum path difference where going
any further will result in the waveforms being more than one wavelength off and thus useless for
measurements. My knowledge of AOM’s went from nothing to well-informed over the course
of a month. The need for modulation was an important lesson since without it, there would be no
waveforms, just flat lines. As for the speed of light, I will not be able to tell my family I
19. Bishop 19
measured it perfectly, but will throw them a copy of An Introduction to Error Analysis to show
my value was within the margin for error.
References
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/indrf.html
http://www.ies.org/lighting/science/
Sarton, George. Ancient Science through the Golden Age of Greece. pg. 248: Courier,
2012. Print.
http://www.speed-light.info/measurement.htm
http://www.merriam-webster.com/dictionary/aberration
http://huntington.org/exhibitions/beautifulscience/timelines/light_web.html
http://www.speed-light.info/angels_speed_of_light.htm
http://www.saburchill.com/physics/chapters3/0007.html
i
Sarton, George. Ancient Science through the Golden Age of Greece. pg. 248: Courier, 2012. Print.
ii
Ibid
iii
http://huntington.org/exhibitions/beautifulscience/timelines/light_web.html
iv
Sarton, George. Ancient Science through the Golden Age of Greece. pg. 248: Courier, 2012. Print.
v
http://www.speed-light.info/angels_speed_of_light.htm
vi
Ibid
vii
Ibid
viii
http://www.speed-light.info/measurement.htm
ix
Ibid
x
Ibid
xi
Ibid
xii
Ibid
xiii
Ibid
xiv
http://www.merriam-webster.com/dictionary/aberration
xv
http://www.speed-light.info/measurement.htm
xvi
http://www.saburchill.com/physics/chapters3/0007.html
xvii
Ibid
