How does different particle size account for different colors? I understand how objects have color in terms of absorption and reflection; however, in stained glass, various nano-particles can have different colors depending on the particle size. As described in this link: http://www.nisenet.org/sites/default/files/catalog/uploads/2474/stainedglasscart_classpresentation_jan10.ppt.pdf 
What accounts for the different colors here? I suspect that it may be due to Rayleigh scattering similar to what makes the sky blue, but I'm not sure. 
Thanks.
 A: In case of metallic nano-particles, the color is determined by location of the localized surface plasmon resonance (LSPR) peak in the spectrum of the nano particles.
Localized surface plasmon resonance is a collective excitation of electrons, which are electrodynamically coupled to each other. Essentially, if a bunch of electrons are at the left side of the particle, they feel force towards the right side of the particle to lower their potential energy. It is like a swing or a spring, and it has a characteristic frequency.
Rayleigh scattering nor Mie scattering (with uniform dielectric function) cannot properly describe the size effect of plasmon resonance. (Rayleigh scattering is just an approximation to Mie scattering). Mie scattering is just solving the Maxwell equations on a particle. If one assumes a constant and local dielectric function across the particle, the solution to Maxwell equations will have a discontinuity in the displacement field between the particle and vacuum indicating a surface charge. The width of this surface charge is infinitesimally small, and it thus fails to reproduce finite size effects. In fact, if Maxwell equations are solved in a quasistatic approximation (meaning that light travels instantly), one gets the same spectrum (except for the intensity) for all particle sizes. 
The nano scale shift in LSPR frequency is caused by several finite size factors. First, there is the spill-out effect. The electrons are not localized within a fixed sphere, but 'spill-out' a certain amount, about a length d (of order of 0.1 nm). This introduces a surface volume of order dR$^2$, compared to bulk volume of order R$^3$, yielding that the surface volume is roughly proportional to 1/R of the total volume (and hence are the surface effects).
Furthermore, there are effects related to quantum confinement. The electrons and holes in a nano particle have discrete energy values due to quantum mechanics, which can introduce multiple peaks but also affect the red/blue shift with respect to particle size.
When decreasing the particle size (roughly from 10nm to 1nm), one can encounter both red shifts and blue shifts in the frequency. This is due to complex interplay between spill-out (and other quantum) effects and various dielectric effects. This is also strongly dependent on the embedding material or substrate.
For example, in noble metal nano particles, the bound localized d-electrons have also a very relevant effect, since they dielectrically screen the oscillating sp-electrons, causing a blue shift (in contrast to sodium clusters which are redshifted due to spill out effects). Essentially, the d-electrons counter the field caused by the conducting sp-electrons in the surface and this screening is size dependent. If you are interested in how to simulate these, we recently did quite large time-dependent density functional theory (TDDFT) calculations to silver clusters, and we obtain a clear dependence (1/R) between the particle size and the localized surface plasmon resonance peak.
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.115431
A: The electrons in metal nano-particles couple to the electromagnetic field, but at the same time, they have eigenmodes of charge oscillations. Therefore, around specific frequencies, the possibility of strong coupling between the electromagnetic wave and the electronic excitations of the particle arise. These combined excitations (that consists of a photonic and an electronic part) are called plasmons. Specifically, these are surface plasmons, because the resonance frequency is not tuned by the bulk properties of the metal but by the shape of the nano-particles (this can be modelled surprisingly well by just considering the classical oscillation of the charges on the particle). The strong coupling between light and the electrons near a plasmonic resonance allows for efficient absorption and therefore coloured glass. If the particles are not spherical the effects will be direction dependent and there will be multiple absorption bands.
Wikipedia has more on this.
