White light is actually full of color, and we can see these colors by shining white light through a prism. For a more detailed explanation, with diagrams, see this HyperPhysics page. For the correspondence of color and wavelength, see What Wavelength Goes With a Color?. Check out this page from the Sloan Digital Sky Survey for an interactive animation showing how color changes with wavelength.
Look at the photo above and see whether the prism bends red light or purple light more.