The physics part: The part that talks about being shiny, I agree, is mainly physics. But proceed in my question, and you'll see how it's a chemistry one.
We know things are shiny if they either produce light, or deflect light well. Producing is not our topic in here, but deflecting is. Metals are considered shiny objects.
Mad scientist (the site, not our fellow friend!) has provided a nice explanation for why metals are shiny: In short, because free electrons (electrons are partially "free" in metals, due to the especial way of bonding) deflect more photons than usual and do not let the inner layers of atoms in the metal absorb them.
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(These three differ in shine because of impurity; not related)
Metals aren't the only materials that are exceptionally "shiny". We are aware of many crystals that are either well-cut or well-formed, which result in total internal refraction and that makes them very shiny too. There's a related question in physics.SE wherein the diamond's shiny properties are questioned.
The organic-chemistry part:
Saying the word "oil" talks about a vast variety of chemicals; therefore, in an attempt to narrow down the question, I only ask about liquid-at-RTP triacylglycerol (the famous triglycerides which exist usually in plants or fish). The chemical structure is as following:
My question is: Organic molecules like these aren't metals, are they?! So since a thorough research (maybe seemingly) didn't get me answers about why these are good light reflectors I'm asking for a way that will allow me to compare the reflectivity of these liquids, primarily from their structural formula. e.g.: Are these liquids "shinier" than water? Why? About water, I would say that for example, Hydrogen atoms in correspondence to the Oxygen atom, make water have hydrogen bonding, which is the main cause of surface tension. Surface tension causes the surface of water to be "smoother" and thus the reflectivity increases. On the other hand, it can't be only about Hydrogen bonding, can it?
(If the answer might be too broad, you may guide me to any resource helping me to find an answer, and that's why I add the tag: reference-request.)
Image sources: http://www.luxrender.net/wiki/images/2/2f/Shiny_yellow_specular_series.jpg ; http://library.med.utah.edu/NetBiochem/FattyAcids/7_2.html ; http://guweb2.gonzaga.edu/faculty/cronk/biochem/images/triglyceride.gif
