Why would you use a prism?

Answer 1

The answer depends on whether you mean a transparent prism or a prism made of any material. The answer below is for optical prisms.

You would use it to break up a beam of light into a spectrum. This can be to study the chemical composition of the substance radiating the light or of the subtance (in gaseous form) through which the light passes (spectroscopy). You would use it in astronomy to look for characteristic absorption lines to measure the red shift of stars, galaxies and other stellar objects and thereby estimate their distances (subject to qualifications about the Hubble constant).

You would use it in optical instruments such as cameras, binoculars, microscopes to correct for some of the aberrations introduced by lenses.