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I remembered that shininess of a material is because of reflection, ie surface current responding to light. Mathematically, one can solve Maxwell equations under a relevant boundary condition, with plane waves ansatz. This math only corresponds to situations when the size of the metal surface is way larger than the wavelength of light. What happen if the surfaces are smaller than wavelength of say ~600nm light?

What happen for metals that have domains size less than the wavelength? What happen for small graphene sheets whose edges are passivated by hydrogen, and are shorter than the wavelength? If electrons cannot move across different domains that are shorter than the wavelength, can the material possibly be shiny?

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We say something is shiny when the reflection from it is specular i.e. the angle of reflection is equal to the angle of incidence. Note that it doesn't matter whether the substrate is a metal (i.e. conducting) or not as insulating plastics can also be shiny.

The problem is that objects of around the wavelength of light or small reflect light in all directions. This is known as Mie scattering, or if the object is much smaller than the wavelength we get Rayleigh scattering instead. In both cases light is reflected at a range of angles, not just at the angle of incidence, and the reflection is diffuse rather than specular.

There isn't a sharp transition to specular reflection as the size of the reflecting object increases, so the size at which we would say the object is shiny is a matter of judgement. From personal experience mica flakes of around 10 $\mu$m and larger look shiny so as an order of magnitude estimate I would say the transition is somewhere around ten times the wavelength of the light.

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  • $\begingroup$ "insulating plastics can also be shiny" I always thought shiny plastic are due to conductive conjugated double bonds like solitons in polyacetylene (insulator by band structure but conductive due to domain boundaries). However, I just learned that polymer like Polypropylene can also be shiny, and they have low dielectric constant compared to most other solid. Question: is the limiting factor in practice for shininess most often determined by smoothness of surface, instead of available current? (even low dielectric material with little surface charge can be shiny if its surface is smooth)? $\endgroup$
    – Bohan Xu
    Nov 10, 2022 at 16:16

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