When white light passes through a glass slab and undergoes dispersion, it separates into its constituent colors due to the different refractive indices of each color. This phenomenon is known as chromatic dispersion. However, the reason we don't see the dispersion and the individual paths of the colors within the slab is because of a process called recombination or rephasing.
Inside the glass slab, each color component of white light travels at a different speed and follows a slightly different path due to their varying wavelengths. As a result, the colors spread out and appear to separate. However, upon exiting the slab, these colors recombine and form white light again.
The recombination occurs because the different colors of light undergo different phase shifts as they pass through the glass slab. The phase shift is the amount by which the wave oscillations of the light are shifted. The glass slab introduces a specific amount of phase shift for each color, such that when they exit the slab, the phases of the colors align again and they recombine into white light.
So, while the colors do separate and recombine within the glass slab, our eyes perceive the final result as white light because the recombination happens before the light reaches our eyes. Therefore, we do not observe the dispersion and individual paths of the colors within the slab because the light recombines before it reaches the point of observation.
To see the dispersion and paths of the colors, we would need to view the light after it has exited the glass slab and not allowed to recombine. This can be achieved by using additional optical components like prisms or diffraction gratings that can spatially separate the colors and allow us to observe the dispersion.