The speed of light in a medium has a significant influence on the propagation of electromagnetic (EM) waves. When an EM wave enters a medium, such as a transparent material like glass or water, its speed changes from its vacuum speed, which is approximately 299,792,458 meters per second.
Refraction: The change in the speed of light causes the wave to change direction at the interface between two different media. This phenomenon is known as refraction. Refraction occurs because the speed of light in a medium depends on its refractive index, which is a measure of how much the medium slows down the propagation of light compared to vacuum. When an EM wave enters a medium with a different refractive index, it bends towards or away from the normal (a line perpendicular to the interface), depending on whether the speed of light decreases or increases in the new medium, respectively.
Snell's Law: The relationship between the angles of incidence and refraction is described by Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities (speeds) of light in the two media. Mathematically, it can be written as n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices of the first and second media, respectively, and θ₁ and θ₂ are the angles of incidence and refraction.
Change in Wavelength: The change in speed of light also affects the wavelength of the EM wave. As light enters a medium with a different refractive index, its speed changes, but its frequency remains constant. Since the speed of light is related to the wavelength and frequency by the equation c = λf (where c is the speed of light, λ is the wavelength, and f is the frequency), a change in speed leads to a change in wavelength while keeping the frequency constant. This change in wavelength is known as the wave's phase velocity.
Absorption and Dispersion: Different materials have different refractive indices, and they can also interact with specific wavelengths of light differently. Some materials absorb certain wavelengths more strongly than others, leading to a loss of energy in the wave as it propagates through the medium. Additionally, some materials exhibit dispersion, where the refractive index changes with the wavelength of light. This results in the separation of white light into its component colors, such as in a prism.
In summary, the speed of light in a medium influences the direction of propagation, angle of refraction, change in wavelength, absorption, and dispersion characteristics of electromagnetic waves as they interact with and pass through different materials.