Thin Film Question: Finding Oil Slick Thickness

[bk999]

I was having a bit of trouble with this question:

A thin oil slick of refractive index 1.3 floats on water. When a beam of white light strikes this thin film vertically, the only colours enhanced in the reflected beam seen in air are orange-red (650nm) and violet (430nm). What is the thickness of the oil slick?I've only gotten as far as finding the wavelengths of the orange-red and violet colours in the film:

wavelength soap = (6.5 x 10-7)/1.3
= 500nm

wavelength soap = (4.3 x 10-7)/1.3
= 331nm

I don't know how to substitute these values and get the same answer for the thickness of the oil slick.

 

[G01]

This problem is basically telling you that the middle wavelengths, such as green light are not present in the reflection.

HINT:
How is (qualitatively) this color of light canceled out by the film?
(If you don't know this answer, you may want to re-read the section on thin films in your text.)

 

[GTrax]

Have a look at this link http://en.wikibooks.org/wiki/Waves/Thin_Films

The light speed in the oil is slower than the light speed in air by factor 1.3, the refractive index. The light that takes a trip through the oil slick, and gets reflected, travels through two thicknesses, getting somewhat delayed before it meets up with the light reflecting direct off the top of the slick.

Ordinarily, you might reasonably think that if the path difference between the direct and the delayed light added up to a length enough to bring the light waves back into reinforcing synchrony (for some colour) that is all you need. Here nature is not reasonable! Right here, be aware that strange, counter-intuitive stuff happens. The direct reflected light off the top surface comes away with a 180 degree phase shift, just as if it had itself seen a delay of 1/2 wavelength in air. Elsewhere in this forum, folks can have a challenging time explaining why.

You don't need that. The colours (sorry - colors) will help you figure the wavelengths. Know that after some years of oxidation film buildup, the shiny stainless steel flue pipe on my woodburner stove is yellow near the bottom, going through the spectrum to violet, then starts over again with another spectrum as we look toward the top. As the layer gets thicker, the show gets better. This should help you figure the thickness of that film.