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Johnson 1 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/>. Johnson 2 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>. Johnson 3 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 Johnson 4 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. Johnson 5 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>. Johnson 6 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. Johnson 7 Works Cited: 1. "Measuring the Speed of Light." colorado.edu. N.p.. Web. <http://www.colorado.edu/physics/2000/waves_particles/lightspeed_evidence.html>. 2. Gibbs, Philip. "How is the Speed of Light Measured?."http://math.ucr.edu/. N.p.. Web. <http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html>. 3. "Speed of Light Measurements." speed-light.info. N.p.. Web. <http://www.speedlight.info/measurement.htm>. 4. Kurtis, Ron. "Speed of Light." school-for-champions.com. N.p.. Web. <http://www.school-forchampions.com/science/light_speed.htm>. 5. Kornreich, Dave. "Who first measured the speed of light?."http://curious.astro.cornell.edu/http://curious.astro.cornell.edu/. N.p.. Web. <http://curious.astro.cornell.edu/question.php?number=269>. 6. Stierwalt, Sabrina. "Is the speed of light constant?."http://curious.astro.cornell.edu/. N.p.. Web. <http://curious.astro.cornell.edu/question.php?number=630>. 7. "The Speed of Light." space.com. N.p.. Web. <http://www.space.com/15830-light-speed.html>. 8. Carlip, Steve. "Is The Speed of Light Constant?."http://math.ucr.edu/. N.p.. Web. <http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html>. 9. "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>. 10. "Maxwell’s theory of electromagnetism." oei.ytu.edu.cn. N.p.. Web. <http://www.oei.ytu.edu.cn/physics/jpkc_dcx/kjzl/Electromagnetics/chap02.pdf>. 11. Otis, Arthur. Light Velocity and Relativity. 3rd. Baltimorem Md.: Universal Lithographers, 1963. Print. 12. Serway, Raymond A., and John W. Jewett, Jr. Physics for Scientists and Engineers with Modern Physics. Seventh. Belmont, CA: Thomson Learning Inc., 2008. Print.