How Do We Know the Speed of Light?

The first time the speed of light was mentioned and recorded was by Aristotle when quoting Empedocles, he said that light must take some time to reach the Earth. That statement, however, is quite obviously not very specific. Aristotle himself didnít even seem to agree with that statement. In Two New Sciences Galileo has Simplicio stating this opinion. The wording is a little confusing but more or less Simplicio says, everyday we witness that light is instantaneous; for example, we see a gun fired at a great distance and the flash reaches us right away while the sound reaches our ear sometime later. This also, however, isnít very specific, it simply says light is faster than sound.

The First Experiment

Galileo conducted the first experiment to find out the speed of light. It went like this; he had 2 people far away from each other each with a covered lantern. One person would uncover their lantern and when the other saw it, he would uncover his. Galileo would observe and see if any time lapsed. The 2 people would have to practice this close to each other many to make sure the got used to the reaction time and to eliminate as much human error as possible. Galileo tried this experiment at distances less than a mile but he couldnít detect a time lapse. This doesnít really give much for conclusions except that light travels at least 10 time faster than sound.

Romerís Better Experiment

Ole Romer was a Danish astronomer working at the Paris Observatory. He studied the moons of Jupiter; mostly he studied Io, quite intensely. He realized that Jupiter eclipses Io at regular intervals. He then realized that the for several months the eclipses lagged more and more in time until they were about 8 minutes late. Then he noticed that after they were 8 minutes late, for several months they began getting earlier and earlier until they were about 8 minutes early. The cycle then repeated itself. Romer realized that the time involved for this cycle was just over a year and the eclipses were furthest behind schedule when Earth is farthest from Jupiter and they were the earliest when Earth is at its closest to Jupiter. That means the light being reflected off Io takes longest to reach Earth when earth us farthest away. Using these observations Romer concluded that light takes 22 minutes to cross the Earthís orbit. That was a bit of an over estimation but not too bad for the first estimation ever.

To find the speed of light, it would have to be known what the distance from the earth to the sun is. This was done by measuring how much Mars shifted on the stars in the background when being observed simultaneously from 2 different spots on Earth. Using that, it could be determined how for the Earth is from Mars. And since all relative distances in the solar system had been established already by using observation and geometry it could be figured out how far the Earth is from the sun. Romer said the Earth was between 40 million and 90 million miles away from the Sun. Romer must have then decided on a number very close to the correct value of 93 million because he concluded that the speed of light is 125,000 miles per second. The correct number is 186,300 miles per second but Romerís error can be accounted for if he used his guess of the light taking 22 minutes to cross the earthís orbit instead of using the correct time of 16 minutes.

8 minutes early 8 minutes late

As the Diagrams above show, the point where Earth and Jupiter are closest during their orbits, the eclipse is 8 minutes early. And when they are as far away as possible, the eclipse is 8 minutes late.

A More Appealing Experiment

The problem with Romerís experiment is that it doesnít have the appeal of two guys with lanterns, like Galileo had. Itíd be nice to be able have a good experiment that can be done entirely right here on our home planet. With out all the telescopes and observing minute changes in the background behind Mars. This problem of appeal was solved by 2 French men in 1850, Fizeau and Foucault. These men werenít working together though, there was 2 separate experiments. The first was by Fizeau. He made an apparatus in which a beam of light shone through a rapidly spinning wheel with many teeth. This way the "lantern" was rapidly and continuously being covered and uncovered. And instead of a second lantern far away Fizeau used a mirror to reflect the beam back at itís source. The wheel could be set up so one tooth would pass by the light every ten-thousandth of a second. The idea was that the blip of light would leave through one gap in the teeth, hit the mirror and is reflected back towards the light.




Fizeauís Experiment Foucaultís Experiment

 

 

 

 

 

 

The Final Experiment

None of the experiments up to the point Iíve explained were very accurate. Polish scientist Albert Michelson was going to change. In 1877 Michelson was living in the U.S. and was a teacher. He decided to further test the speed of light. Michelson thought heíd use Foucaultís experiment. The reason this experiment wasnít incredibly accurate when Foucault did it was because he had only 60 feet between the rotating mirror and the far mirror. With how fast light travels that doesnít leave too much time for the rotating mirror to change its angle and thus makes it very difficult to measure with any degree of accuracy how fats the light is travelling. Michelson made his apparatus with 2000 feet between the rotating mirror and the far mirror, which he measured to one tenth of an inch. To do this correctly Michelson then had to acquire very high quality lenses to focus the light. He was granted $2000 from his father in law and he could get these lenses. Michelson conducted his experiment and his results turned