Final answer:
The velocity of light in a medium depends on light's wavelength, leading to variable refractive indices for different colors due to refraction. Light slows down and refraction occurs more in materials with a higher refractive index, and dispersion occurs because refractive index depends on wavelength.
Step-by-step explanation:
The velocity of light in a medium depends on the wavelength of light and thus different colors travel with different velocities in a medium. Therefore, the refractive index of a medium is variable for different colors. When light changes speed at a boundary between two media with different refractive indices, it also changes direction, a phenomenon known as refraction.
For example, when a ray of light passes from air into water, it travels more slowly in water, because light interacts with the atoms in a material. This change in speed causes the light to bend or refract. The extent to which the light bends depends on the refractive index of the two media involved. The refractive index is higher for materials in which light travels more slowly, such as water or diamond, compared to air.
The refractive index is also dependent on the wavelength of the light. This dependency results in the dispersion of light, where white light splits into its constituent colors, much like through a prism, with violet light bending more than red light because it has a shorter wavelength and thus a higher refractive index in a given medium.