How do scientists measure the speed of light? We don’t. No, seriously, we don’t measure the speed of light (which always refers to the speed in a vacuum). We know exactly what the speed of light is.
It is: c=299792458ms−1
And that is absolutely 100% accurate, with no measurement errors. But Jack, I hear you say, what are you talking about? The reason we know that that’s exactly the speed of light is that we defined it to be that number. We then take our definition of a second (the length of time for a certain number of periods of the radiation emitted in hyperfine transitions in caesium-133), and from that, we define a meter. So the thing we would be measuring is what a meter is.
We use the speed of light as a fixed velocity, from which all observers can define their own length scale. To measure the speed of light would require an external definition of what a meter is, and since about the 1970s, we don’t have one.
If you did want to measure the speed of light using this external distance reference, it’s easy to test; you just release a light pulse at t=0 towards a mirror and then time how long it takes to get back to you. This is the exact principle that radar/sonar work on (although again, they measure the distance knowing the speed—but it works either way around).
The meter was originally defined after the French Revolution, in about 1799. It was defined as 1⁄10,000,000 the distance between the equator and the pole.
The “meter” was formally defined from 1889 as the length of a platinum rod, held in a vault in Paris.
From this definition of a meter (and an old definition of a second), we measured (using the mirror-timing method, or based on astronomical observations) the speed of light to be about 299792458, plus a non-integer bit, and error bars from the measurement errors.
Eventually, we realized that having a meter defined by something there was only one of was a bit annoying. So, we attempted to define it in a way that anyone could replicate without having to refer to a “standard object.” Therefore, we redefined the meter—using the speed of light.
The official definition of a meter today is:
1⁄299792458 of the distance travelled by light in a vacuum, in 1 second.
Using the caesium definition of a second.
Therefore, this was exactly equivalent to defining the speed of light to be the number given above. We chose that number (and not a more convenient number like 300,000,000), because that number changed the definition of a meter by only a fraction of a fraction of a percent, but made everything all nice and integer-y.
A consequence of using this definition is that any attempt to measure the speed of light is cyclical; you must use a “meter” to measure it at some point, which relies on the speed of light.
Therefore what you actually do now, when you “measure” the speed of light (in a vacuum), is actually “measure how accurate your measuring instruments are.”