Light-matter interaction and an object's appearance I am taking a course in Computer Graphics, and the teacher said we could put materials in there main categories:


*

*mirror like

*glossy or specular

*diffuse


He suggested that the law of reflection is immutable and applies to all types of surfaces but that glossy and diffuse surfaces appeared the way they do because of their microstructure. The roughness of these surfaces causes light rays to be reflected in random directions, thus blurring incoming light. So far, so good.
He also insisted on the idea that surfaces (expected in the case of metals) reflects the incident light color. In other words, if the incident light striking a mirror is white, reflected light is white (and not yellow as it is with gold, but again metal is a different case).
What I don't understand is that: if you use "roughness" to explain why some materials are shiny and others diffuse, diffuse surfaces too reflect incoming light color as mirror surfaces do. Therefore if mirror like surface do not have a color of their own (since they only reflect the incoming light color) so should diffuse surfaces. But diffuse objects have a color of their own (which mirror surfaces don not have). Thus, there's a flaw in the reasoning which I can't resolve.
I understand the object's color comes from the fact that electrons making up the atoms the material is made of, selectively absorb photons of some specific wavelength, and reflect the others. However does it mean it reflects these photon always in the mirror like direction? How and why does that happen that way if this is the case?
I am trying to put in one single pictures all the pieces of the puzzle together. Light can only be either reflected or refracted, however objects are coloured because they absorb some light frequencies, but I am told that "mirror reflection" does not affect the incident light color (in other words, that the reflected light color and the incident light color are the same in the case of mirror like reflections).
I am totally lost and would really appreciate if someone could shed light on this mystery.
 A: There's quite a lot to say about this, 18490.  The tl;dr for Mythbusters fans is at the end.


*

*Most materials are somewhat transparent.
This is why you often need two or three coats of paint on a wall.  The light enters the material, travelling many microns before it is eventually absorbed or scattered back.  The result is usually that most of the light is absorbed (most materials are rather dark), and the light scattered back is diffuse and usually coloured.  This is true even if the surface is smooth.

*Even if the material is somewhat transparent, or completely transparent like glass, there will be some reflection at the surface due to the difference in refractive index between the material and the air, but this is usually only a few percent.  This occurs by a different mechanism, and is not strongly dependent on wavelength.  If the surface is smooth you get a glossy appearance, but you can still see the underlying colour.

*Metals on the other hand are very opaque.
Light is basically reflected from right at the surface, penetrating only a few nanometres into the metal.  The mechanism of reflection is different again - involving the whole material, not requiring scattering by individual atoms or larger particles.  Therefore they often reflect a large proportion of the light and are rather white (ie silvery, reflecting all wavelengths).  Gold is of course gold coloured.  If the surface is smooth, then they will act as mirrors.

*But what about snow and white puffy clouds?  These are made of billions of tiny ice crystals or water droplets.  Each one reflects some of the light hitting it because of the refractive index effect.  Because water and ice are transparent, light can enter the cloud, be bounced around a few times by some droplets, pass right through others, and still exit without being absorbed.  Something similar happens in other white powders, like the titanium dioxide used in paints.  Result: perfect matte whiteness.
Item 1 leads to the well-known aphorism, "You can't polish a turd."  Mythbusters proved, however, that you can!

A: Good question.
The key is to realize that a mirror-like surface send rays of light into your eyes directly from the source; they just bounce simply off of the mirror.  What you see is the source, and the color of the source.
Not so for a diffuse object.   In this case light from the source hits the mirror and does not bounce directly into your eye.  It goes everywhere.  
Now turn this around:  where did the light that enter your eye come from?   It comes from all sources nearby.  The nearby lamp, the ceiling, the vase of flowers... every object that has light coming from it.  The light from each of these sources hits the diffuse surface and scatters in all directions.  Some small part of the light from each source is scattered in the direction of your eye.  The light that enters your eye is a very mixed up combination of light, containing colors of all of those sources.
In an average room, all colors of light are available from all of the various sources.  When added together, they make something whitish.  When that "white" light hits the diffuse surface, indeed, some colors are absorbed.  So what you see is the color of the diffuse object itself.  Well, nearly that color, because the incoming light won't be perfectly white.
If you were in a dark room with just red lamps providing light, then, of course, all of the scattered light it red and the object will appear to be red regardless of what the color of its pigments are.
