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Dispersion is the phenomenon in which different wavelengths or colors of light travel at different speeds in a medium, leading to the splitting of light into its constituent colors. This happens because the refractive index of a transparent medium varies with the wavelength of incident light.

In a transparent medium, such as glass or water, light waves interact with the atoms or molecules of the medium. When light enters the medium, its electromagnetic field causes the electrons in the material to oscillate, which in turn creates an oscillating electric field. This interaction between the light and the electrons causes the speed of light to slow down within the medium. Since the refractive index (n) of a medium is the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v), and is given by n = c/v, a change in the speed of light results in a difference in refractive index for different wavelengths. In most transparent media, the refractive index decreases as the wavelength of the incident light increases. Consequently, shorter wavelengths (blue/violet light) are slowed down more and have a higher refractive index than longer wavelengths (red/orange light).

The phenomenon of dispersion causes light to bend or refract by different amounts as it passes through a transparent medium, leading to a separation of colors. This is the reason why we observe a spectrum of colors in a prism, where white light entering the glass is split into its constituent colors. Another common example of dispersion is the formation of rainbows, where sunlight gets dispersed into a spectrum of colors after passing through water droplets in the atmosphere. Dispersion can also lead to chromatic aberration in optical instruments, such as lenses and telescopes, causing blurry images due to the different focusing points for different wavelengths of light.