In general, the difference in the speed of light in other mediums is ignored.
Earlier thoughts: How fast is the speed of light?
Hundreds of year ago people thought light travelled instantaneously. They thought so because after a military artillery fired at a large distance, they saw the flash immediately, but sound took a noticeable delay before you heard it.
Even in 1600 A.D. the famous Johann Kepler believed that the speed of last was instantaneous. According to him the vacuum of space did not slow the speed of light down.
Galileo was correct in saying that all this proved was that light moved faster than sound - not necessarily instantaneously.
Galileo - speed of light measured using lanterns
Galileo Galilei suggested in 1638 and carried out experiments in 1667 to try measure the speed of light. ( Pictures of Galileo Galilei )
Two people had to stand at least a mile apart. They both had covered lanterns. When one person uncovered his lantern, the other person had to uncover his lantern when he saw this. A third person measured the time between when the first and second lanterns where uncovered.
Repeated experiments failed to accurately measure any time interval between when the first and second lanterns were uncovered. They could only say that light travel at least ten times faster than sound.
Olaus Roemer - speed of light measured using the moons of Jupiter
In 1676, Ole Roemer made the first accurate measurement of the speed of light using Jupiter's moons.
Roemer made a detailed study of the frequent eclipses of Io by Jupiter. This enabled him to accurately predict when the next eclipses will occur.
However, over a period of months, Roemer's predictions were steadily off by longer and longer intervals of time. His predictions were eventually off by eight minutes.
Even stranger was the fact that these predictions then became more accurate, till they were correct again. This strange cycle repeated itself again and again with great regularity.
Roemer realized that this time difference was caused by the difference between the distance between the earth and Jupiter. When Jupiter was closest to earth, the eclipses happened on time. The further Jupiter was away from the earth, the later the eclipses became - light had a longer distance to travel to earth and this took longer.
The size of the earth's orbit and Jupiter's orbit around the sun was known at that time.
Roemer used these figures to determine the distance between the earth and Jupiter for all his observations.
Roemer used these somewhat inaccurate distances (as it was known in 1675) to calculate the speed of light to be around 200 000 km/sec.