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It was a few days ago, and there was a very heavy storm(currents were flowing beside the sidewalks as normal). I became intrigued by a thin film of gasoline that got caught in one of the currents. The visible colors of course changed by my angle of incidence, yet because there was a current, the thickness of the film also changed, as it spread out and moved along with the water. I would like to make something of this. How did an unchanged angle of observation result in so many different changes in which colors were the most visible at a certain time?

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sounds like you answered own question for the most part. The reflection you're seeing with your eye is based on the reflection on the surface of the fluid or within layers of the fluid.

White light was scattered onto the fluid. Certain wavelengths created an interference pattern and could not escape the thin film region (which as you described, the thickness was controlled by the current).

The wavelengths that could escape from that thin layer, which were not total internally reflected, are the ones that you observed.

For more information look up Total Internal Reflection. It's based on the index of the 3 layers that you're considering....Water, Oil, Air. The oil in some ways acts as a waveguide to propagate light.

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  • $\begingroup$ Right. But my question had to do with taking a differential like approach to the problem. What wavelengths were visible as the flow of the current moved the varying thicknesses of oil across the water's surface. And as that happened, how would the thickness of the oil itself change (and thus change which colors were visible). $\endgroup$
    – Gödel
    Commented Jun 20, 2014 at 0:38
  • $\begingroup$ @NaturalPhilosopher you are talking about thickness changes of submicron scale in a layer on top of a fluid in motion. Even the tiniest motions are going to show up as a perturbation of the layer thickness and / or local angle of incidence. Perhaps shut yourself in a room with no draughts and set up the phenomenon in a controlled way: beaker of water with some oil on top and a well mounted light source. See whether, by being very still, you can get the oil to make static colour patterns. My guess is you can, but even the tiniest draught (e.g. from your breath) will beget a colour change. $\endgroup$ Commented Jun 20, 2014 at 0:45
  • $\begingroup$ Thank you so much sir! I wanted to find patterns in this phenomenon, but it seemed very complicated until that suggestion. The only problem would be measuring the thickness of the film without adding too much "noise" into the mix. How could I do that? $\endgroup$
    – Gödel
    Commented Jun 20, 2014 at 0:50
  • $\begingroup$ Sean, you seem to be correct, but I think this answer could use some improvement, like use a diagram to explain why the white light is interfering in the thin film waveguide, etc. $\endgroup$
    – daaxix
    Commented Jun 20, 2014 at 3:47
  • $\begingroup$ I am familiar with this occurrence, perhaps it was my fault for not stating what I already knew concerning the question. My question had to do with a differential equation that could describe the changing color patterns from a change in thickness as the oil flowed on top of the moving water. $\endgroup$
    – Gödel
    Commented Jun 20, 2014 at 10:43

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