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Calculating the speed of light!

The speed of light is a universal constant, which is central to many things in physics. If we want to know what the speed of light is, we can just look it up and know precisely that the speed of light is up to 9 digits long - 299,792,458 m/s. This is so fast, it takes about 0.13 seconds for light to travel around the world.


However, such an accurate value of the speed of light was not known all the time. Galileo Galilei was the first person who tried to quantify the speed of light; he got his assistant to stand on top of a hill, who would open and close a shutter in front of his light, and Galilei would stand as far as possible, and would try to manually measure the speed of light with his timer — his pulse. He failed to succeed with this method, because he needed to have either extremely large distances or a method of measuring time with large precision. For some time after Galileo’s unsuccess, it was thought that the speed of light was instant. The first known person who succeeded in measuring the speed of light was actually an astronomer, Ole Rømer, all the way in 1676. Moreover, he had a much different goal in his mind - to receive the reward of 15000 English pounds for discovering a method for precisely measuring the longitude on a ship. The idea of measuring longitude is rooted in time - setting a clock to noon (when the sun is precisely above your head) in London and then traveling to another place, and measuring the time difference at noon in that place. As easy as it sounded, it was impossible to achieve at the time - the only clocks available were mechanical clocks with pendulums, which could not work precisely on the board of the ship due to the rowing. For such a precise clock, the astronomers turned to the sky, and Rømer looked specifically at one of Jupiter's moons - Io.

When observing Io from Earth, we can see it most of the time due to sunlight being reflected from it. However, sometimes Io is not visible when it goes “behind” Jupiter, and the sunlight reflected from Io does not reach earth. Since the period of revolution was measured, astronomers could predict when Io will disappear into Jupiter's “shadow.” Rømer measured this two times, and realized that on his second measurement Io appeared later by 22 minutes, and from this Rømer figured that Io appeared later due to light taking more time to travel, since the rotation of earth and Jupiter around the sun made the distance between them larger.

After calculating the difference in the distance, Rømer measured the speed of light to be around 227 000 km/s, which is off by around 30%, but at his time the first estimation of the speed of light was a groundbreaking discovery. The first method of measuring speed of light using mechanical constructions was invented by Armand Fizeau. He shined the line onto a mirror, through which the light rays would reflect in another direction and go through a focusing lens, which is something I have talked about in one of my previous articles. After that lens, the light would travel for 8 kilometers until it met another focusing lens, which focused the light down to another mirror. From that mirror, the light would bounce back and travel the same distance, returning back into the human eye through the final lens. However, between the first mirror and lens Fizeau also placed a toothed cogwheel, the speed of which he could manipulate.

If the cogwheel was spinning slowly, the light wouldn’t disappear since it had enough time to travel back before the next tooth would appear. When the cogwheel is spinning, the light keeps appearing and reappearing, like the flickering of a switch. As we increase the velocity, the flickering increases, but then at a certain terminal speed the flickering stops, since the returning light is too slow to return before the next tooth of the cog appears. Such technique allowed Fizeau to measure this speed of light as 313 000 km/s, which was much more accurate and closer to the real value than Rømer’s estimation was.


Another worthy mention is the simple wave speed formula. In one of my articles, I talked about how the speed of a wave can be measured by knowing its frequency and wavelength. If we know these parameters, we can identify the speed of light by multiplying the wavelength by the frequency, which is the technique that can be used in more modern computations of the speed of light. A lot of other modern computations for the speed of light also use mirrors and lenses, but the systems are much more complicated and the detecting technology is much more accurate. One interesting method can be viewed here.

Another way the speed of light was measured was using two other well-known constants - vacuum permittivity and vacuum permeability. These constants are used to evaluate the speed of electromagnetic waves, but as it turns out, they actually travel at the speed of light!

 

https://www.youtube.com/watch?v=H9kZTm4Xm-8 - a video that demonstrates the method from the link above in simpler terms.

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