The speed of light in a medium does not depend on the frequency of the incident light. The speed of light in a given medium is primarily determined by the properties of that medium, such as its refractive index.
According to the universal speed limit of light in a vacuum, the speed of light is constant and equal to approximately 299,792,458 meters per second (denoted as "c" in physics). However, when light passes through a medium other than a vacuum, such as air, water, or glass, its speed changes due to interactions with the atoms or molecules of the medium.
The speed of light in a medium is typically lower than the speed of light in a vacuum, and it is given by the equation:
v = c / n
where "v" represents the speed of light in the medium, "c" is the speed of light in a vacuum, and "n" is the refractive index of the medium. The refractive index is a dimensionless quantity that indicates how much a medium slows down the speed of light compared to its speed in a vacuum.
The frequency of the incident light, on the other hand, remains unchanged as it enters a different medium. The frequency of light corresponds to the color or energy of the light and determines its wavelength (the distance between successive peaks or troughs of the light wave). When light passes from one medium to another, its frequency remains constant, while its wavelength changes due to the change in speed. This phenomenon is described by the equation:
v = λf
where "v" represents the speed of light, "λ" is the wavelength of the light, and "f" is the frequency of the light.
So, in summary, the speed of light in a medium is determined by the properties of that medium, while the frequency of the light remains constant as it enters a different medium.