The experimental proof that the speed of light is lower in a denser medium compared to a rarer medium is credited to the Danish physicist Hans Christian Ørsted. Ørsted conducted experiments in the early 19th century that demonstrated the phenomenon of refraction, which is the bending of light when it passes from one medium to another.
The specific experiment that provided evidence for the change in speed of light was conducted by Ørsted in 1815. He used a beam of light that passed through a glass prism. By measuring the angle of deviation of the light beam as it entered and exited the prism, Ørsted was able to show that the speed of light is slower in the denser medium of the glass compared to the rarer medium of air.
Later, other scientists such as Augustin-Jean Fresnel and Sir Isaac Newton also made significant contributions to our understanding of light's behavior in different media. Fresnel developed a mathematical theory of light's behavior during refraction, while Newton proposed a particle theory of light that explained refraction in terms of the interaction between light particles and the medium.
Overall, the experimental work of Hans Christian Ørsted and the subsequent contributions of other scientists helped establish the principle that light travels slower in a denser medium than in a rarer medium.