opticsphotonsreflectionvisible-light
Light falls on a surface. Some wavelengths get absorbed. The other are reflected. The reflected ones are the colors that we perceive to be of the surface.
What is the property that determines, what wavelengths are reflected and what are absorbed? Is it electronic configuration of the object on which the light falls?
If yes, then if we know the electronic configuration of a surface can we make a model, which will predict the color it will show?
The human eye has three types of colour receptors, called cones, that respond to red, green and blue light. Your brain interprets the colour based on the signals from these cones.
For example suppose you're looking at red light. Only the "red" cones will generate a signal and your brain interprets this as red. Suppose now you're looking at a mixture of red and green light. This time the red and green cones generate signals while the blue cones do not, and your brain interprets this as yellow. If there is no light entering the eye none of the cones generate a signal and your eye interprets this as black.
Some colours are pure, that is they consist of light with only a single wavelength, but most colours are mixtures of light with lots of different wavelengths. There are lots of ways scientists measure colour e.g. the RGB system, but actually this turns out to be a surprisingly complicated thing to do because many measurement schemes can't measure all possible colours. Have a look at http://en.wikipedia.org/wiki/Colour for more info.
Finally, to take you example of a red apple: the apple is red because it reflects red light but absorbs other colours. If I shine white light from a torch onto the apple only the red light is reflected and enters my eye, so I see the apple as red. Suppose I shine pure blue light (wavelength about 450nm) onto the apple, what will I see. Well the apple will absorb the blue light so no light enters my eye, and the apple looks black.
Basically: What intrinsic property causes the differences between how the varying wavelengths of light are reflected at the atomic scale? Also, how do photons factor into this?
These are absorption lines in the solar spectrum
Fraunhofer lines coincide with characteristic emission lines identified in the spectra of heated elements.6 It was correctly deduced that dark lines in the solar spectrum are caused by absorption by chemical elements in the Solar atmosphere.
Emission lines of Iron are shown below.
If you have some physics background you will know that both these spectra depend on photon emission and absorption by the electronic states around atoms and molucules.
As there are many elements in the sun part of the observed continuity of the spectrum is due to the overlap of frequencies and the multiple possible states for each atom and molecule to absorb/emit photons.
There exists also continuous emission of photons when electrons ( charged particles) are accelerated or decelerated in external spill over electric and magnetic fields that exist around all atoms and molecules. This spectrum, called black body, will be continuous, and is what one sees in an incandescent lamp or very hot iron; photons are emitted continuously by all bodies , even though not in the visible spectrum.
So the role of photons is crucial to all electromagnetic radiation, including that from our sun. As an ensemble they form the classical light wave, the creation process is a quantum mechanical one involving photons.
Reflection is again an interaction of the individual photons of the beam with the material they impact. The frequencies that are not absorbed will define the color of the material that scattered the beam. So photons are crucial to defining the colors we see.
The photons are coherently scattered by the field of the electrons of the atoms and molecules of the scatterer. The classical view of an electromagnetic wave can be shown to coincide with the quantum mechanical one and is much easier in calculating the behavior of beams, which are huge ensembles of coherent photons.
Best Answer
This question is too broad. It involves ALL the objects in the universe which have a surface, i.e., everything. I'm going to avoid giving a lecture here.
In some liquids and most gases the electronic structure of each individual atom or molecule is enough to describe their spectra.
The "property" you are looking for in the case of solids is the band structure. See this page for a good introduction, specially the section about insulators and dopings. People arrived at the point where they needed to describe the spectrum of solids by (macroscopic) parameters instead of the atomic and band transitions (on top of that, sometimes you have to consider relativistic corrections): Absorption, and scattering or fluorescence. See this page for a shorter explanation, note that this is valid not only for visible light. For normal incidence, backward scattering is "reflection", while forward scattering is "transmission". The color you see will also depend on the flatness of the surface, but this does not affect the physics of the light scattering.
One interesting fact is that you could see (actually you can't, this holds for X-rays) that light gets "reflected" to more that one spot because of Bragg's law.
Lastly, according to your OP title, you might consider reading more about gratings, in which the surface is worked to specifically manipulate colors.