The speed of light in a vacuum was first determined by Danish astronomer Ole Rømer in the late 17th century. Rømer made this discovery while studying the moons of Jupiter. He noticed that the observed timings of the moons' eclipses appeared to vary depending on the relative positions of Earth and Jupiter in their orbits. Rømer correctly attributed this variation to the finite speed of light.
The formal establishment of the speed of light as a fundamental constant in physics came later with the work of James Clerk Maxwell in the 19th century. Maxwell's equations, which describe the behavior of electric and magnetic fields, provided a theoretical framework for understanding electromagnetic waves, including light. Maxwell's equations predicted that the speed of these waves in a vacuum was approximately equal to the speed of light.
The experimental verification that the speed of light is indeed a constant and not dependent on the observer's motion was provided by the famous Michelson-Morley experiment in 1887. Albert A. Michelson and Edward W. Morley designed an experiment to measure the difference in the speed of light in different directions as Earth moved through the hypothetical "luminiferous aether," a medium believed to be responsible for the propagation of light at the time. However, the experiment yielded null results, showing that the measured speed of light remained the same in all directions relative to Earth's motion.
These findings, combined with subsequent experiments and theoretical developments, led to the development of Einstein's theory of special relativity in 1905. Special relativity postulates that the speed of light in a vacuum, denoted by "c," is constant for all observers, regardless of their relative motion. This fundamental principle has been extensively confirmed through numerous experiments and observations and is now a cornerstone of modern physics.