Download Speed of Light Measurements

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Cameron Johnson
Physics 223
May 31, 2013
Speed of Light Measurements
How to measure of the speed of light has been a topic of scientific study since the time
of the ancient Greeks. At that time and up through the early 17th century, many scientists
believed that the speed of light was infinite meaning that it traveled from point to point
instantly. In fact, one of the most influential philosophers and scientists in history, Aristotle,
believed this to be true. Today, it is commonly accepted that the speed of light in a vacuum is
299,792.458 km/s 1. But how did we find this value? What techniques were used? How was it
measured to this accuracy?
The first attempt to measure the
speed of light is often credited to Italian
philosopher and scientist Galileo Galilei in
1638. Though it was still common belief that
the speed of light was infinite, Galileo
disagreed and thought that he could disprove
this by actually measuring it. His experiment
consisted of himself and an assistant standing
on the top of separate hills one mile apart.
Figure 1: Example of Galileo's Method. N.d. Graphic. N.p.
Web.<http://scientopia.org/blogs/skullsinthestars/2008/03/21
/relativity-measuring-the-speed-of-light/>.
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Each held a lantern that could be covered and uncovered quickly. The idea was that at first,
both lanterns would be covered. Galileo would then uncover his lantern and as soon as his
assistant saw this, he would uncover his lantern as well. Using some kind of timing device,
likely a water clock in which the quantity of water that emptied from a reservoir signifies the
amount of time that has passed, he would be able to determine the amount of time that it took
for his assistant to uncover his lantern. With this information plus knowing the distance
between the two hills, Galileo thought he would be able to determine the speed of light by
simply dividing the distance by this interval of time. Unfortunately, his experiment was
unsuccessful because the actual speed of light was far too fast for him to determine in this way
because the distance was not nearly far enough. In fact the distance between the lanterns
would have to be on the order of at least thousands of kilometers for a human to be able to
detect a noticeable time delay between the uncovering of the lamps. Though this experiment
was mostly unsuccessful, Galileo deduced that the speed of light was at least ten times faster
than the speed of sound 3.
In 1675, Danish astronomer Ole Roemer inadvertently stumbled upon a way to actually
measure the speed of light. While observing the shadows of the moons of Jupiter, he found
Figure 2: Example of Roemer’s Method. N.d. Graphic. n.p. Web.
<http://www.daviddarling.info/encyclopedia/S/speedlight.html>.
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that the moon Io made a complete orbit every 1.76 days. What was strange was that though
the total time the orbit took was consistent, at certain times of the year, Io’s position around
Jupiter was behind schedule, and at other times, it was ahead of schedule. It appeared at first
as though Io was actually speeding up and slowing down in its orbit. Through more
observations, Roemer found that Io was ahead of schedule specifically when the Earth and
Jupiter were closer together, and that it was behind schedule when they were farther apart. He
then realized that this must be because light actually does take time to travel between points.
When the Earth and Jupiter were closer together, it took less time for the light from Jupiter to
arrive on Earth, thus Io appeared to be ahead of schedule. Likewise, when the Earth and Jupiter
were farther apart, it took more time for the light from Jupiter to arrive on Earth, thus Io
appeared to be behind schedule. Given the change in distance between the Earth and Jupiter,
and the change in Io’s timing, Roemer was able to determine the speed of light to be 214,000
km/s. Though this value is not very close to what the now accepted speed of light is, it was a
decent approximation for the time because it was on the correct order of magnitude even
though the actual distances between planets were not accurately known 2.
In 1728, English astronomer James Bradley devised an experiment to measure the speed
of light that ended up being very close to the accepted value of today. His method involved
observing stellar aberration which is caused by the apparent displacement of stars with respect
to the Earth orbiting around the Sun. Essentially, stellar aberration is the approximate ratio of
the orbital speed of the Earth around the Sun to the speed of light. Bradley found that, while
observing the star Draco, its apparent position changed during the course of the year. Using
the known orbital speed of the Earth around the sun and measuring the stellar aberration
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angle, he was able to determine that the speed of light was in the vicinity of about 301,000
km/s 2.
Figure 3: Example of Bradle'ys Method. N.d. Graphic. n.p. Web.
<http://www.conspiracyoflight.com/Esclangon/Aberration_and_Esclangon.html>.
In 1849, French physicist Hippolyte Louis Fizeau formed the first successful speed of
light measurement that didn’t involve using heavenly bodies. His experiment involved a rapidly
rotating wheel of variable speed and a mirror located more than five miles away. Fizeau shined
a beam of light through the gaps between the teeth of the wheel toward the mirror which in
turn reflected back from the mirror through the same gaps on the wheel. Fizeau then increased
the rotation speed of the wheel until the gaps moved so fast that the reflected light could not
pass through the same gaps before they moved out of the way. By using the rotation speed of
the wheel he was able to determine the time it took for the light to travel from the mirror to
the wheel. He then divided the distance from the wheel to the mirror by this time interval and
determined the speed of light to be 313,000 km/s 3.
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Figure 4: Example of Fizeau's Method. N.d. Graphic. n.p. Web. <http://spie.org/x32833.xml>.
In 1862, another French physicist, Leon Foucult, expanded on Fizeau’s approach and
came up with the most accurate measurement of the speed of light yet. His method consisted
of a rotating mirror and a remote fixed mirror which faced the rotating mirror. He shined a
beam of light onto the rotating mirror which reflected to the fixed mirror and then back to the
rotating mirror. Because of the rotation of the first mirror, the angle of the light reflected back
to it from the fixed mirror
had shifted slightly. Foucult
was able to measure this
angle and by using this
measurement and the
distance between the two
mirrors, he was able to
determine the speed of light
Figure 5: Example of Foucult's Method. N.d. Graphic. n.p. Web.
<http://www.pas.rochester.edu/~pavone/particlewww/teachers/demonstrations/FoucaultDemonstration_files/image002.jpg>.
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to be 299,796 km/s, which is incredibly accurate for the time 3.
In 1864, James Clerk Maxwell proposed his theory of electromagnetism that completely
changed the way in which the speed of light could be measured. Essentially, his theory showed
that light is in fact electromagnetic waves and only made up a small part of the electromagnetic
spectrum. This opened up new ways to measure the speed of light in that scientists could now
measure the speed of electromagnetic waves that weren’t necessarily light, to determine this
speed 10. In addition, in 1888, Heinrich Hertz created and measured electromagnetic waves in
his laboratory and found that they traveled at the same speed as visible light which also
suggested that they are the same 1.
In 1857, Wilhelm Weber and Rudolf Kohlrausch were able to use this new information
about light and electromagnetism to find the speed of light by measuring the magnetic
permeability and electric permittivity of free space. Using this same method, Rosa and Dorsey
were able to calculate the speed of light to be 299,788 km/s in 1907 which was the most
accurate measurement yet. During the next fifty years, more accurate methods were
developed which allowed for more accurate measurements of the speed of light. In 1958, K. D.
Froome conceived an experiment using a microwave interferometer and a Kerr cell shutter and
calculated the speed of light to be 299.792.5 km/s. The development of lasers in the 1970’s
lead to high spectral stability and accurate caesium clocks which allowed for much more
accurate measurements. By 1970, the speed of light was known within an error of plus or
minus 1 m/s and in 1983, the meter was redefined internationally as the distance light travels in
a vacuum in 1/299,792,458 of a second. This definition of the meter made the official speed of
light in a vacuum exactly 299,792.458 km/s 2.
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3.
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<http://curious.astro.cornell.edu/question.php?number=630>.
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<http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html>.
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"How "Fast" is the Speed of Light?." grc.nasa.gov. N.p.. Web. <http://www.grc.nasa.gov/WWW/k12/Numbers/Math/Mathematical_Thinking/how_fast_is_the_speed.htm>.
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<http://www.oei.ytu.edu.cn/physics/jpkc_dcx/kjzl/Electromagnetics/chap02.pdf>.
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Seventh. Belmont, CA: Thomson Learning Inc., 2008. Print.