How Does a Precipitate Get a Colour?
The 'white colour' is due to the fact that the product does not absorb light in the visible part of the spectrum but forms as many fine crystals which in themselves scatter room lights. So the 'whiteness' is due to the scattering of light back towards your eyes after the light is repeatedly reflected of the many facets of the many crystals in the ppt. If you use red light to illuminate then the 'white colour' will become red. If the ppt is coloured then absorption of light occurs at some wavelengths as well as scattering at all wavelengths.

At the surface of a crystal some small fraction of light is reflected, but with millions of randomly oriented crystals numerous reflections occur. The amount of reflection at each surface depends on the difference in refractive index between the crystal and air for the wavelength of light used. If you could add a solvent say dichloromethane which has  a high refractive index and will probably not dissolve the ppt then the crystals can be made to almost disappear as scattering is now far less.  You can do the same thing with frosted glass beads which, when in air, scatter a lot but in water become virtually invisible.