Question

why white light is separated into different colors when it is passed through a prsm

Answer 1

Due to the phenomenon known as dispersion.
The splitting of a ray of white light into its component colours(VIBGYOR) when it is passed through a glass prism or a water droplet is called dispersion of light.

Answer 2

When white light enters the prism, each kind of light within white light (all the colors) are reflected at different angles because of the different wavelengths. This effectively separates all of the colors present in white light into different bands which we can see as the spectrum.so this is the reason behind the question