Can Fraunhofer Single Slit formula be used in this case?

[catch22]

A question like : A very thin layer of oil is on the surface of a puddle of water. If the layer of oil is 400 nm thick, what frequency of light in the visible part of the spectrum will most strongly be reflected? Given the index of refraction of oil is 1.4.

Can we think of the layer as a single slit with width 400 nm?

 

[Chandra Prayaga]

I am not sure why you thought of that analogy. The situation is that light is incident in a direction perpendicular to the layer of oil. So it is not an application of diffraction at all.

 

[catch22]

I am not sure why you thought of that analogy. The situation is that light is incident in a direction perpendicular to the layer of oil. So it is not an application of diffraction at all.

it only calculates the frequency of THE wavelength that is in a direction perpendicular to the layer of oil?

 

[Chandra Prayaga]

Basically, the situation is this. You have an oil slick on water. From above, you shine light down on the slick. In general, the light would be reflected. But, depending on the thickness of the slick, and the refractive index of the oil, a particular wavelength of light would be strongly reflected. The question is asking for that wavelength.

 

[catch22]

Basically, the situation is this. You have an oil slick on water. From above, you shine light down on the slick. In general, the light would be reflected. But, depending on the thickness of the slick, and the refractive index of the oil, a particular wavelength of light would be strongly reflected. The question is asking for that wavelength.

so what is the proper way to solve for the most strongly reflected wavelength? does it matter what angle of incidence it is to the slick?

 

[Chandra Prayaga]

I would refer you to a topic titled, "Interference of light in thin films" covered in any basic textbook, such as Resnick & Haliday, or Knight.

 

[jtbell]

You can also find many references with a Google search for "thin film interference", including this page and the pages linked from it:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/thinfilm.html

 

[Chandra Prayaga]

You can also find many references with a Google search for "thin film interference", including this page and the pages linked from it:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/thinfilm.html

Yes. The link given by jtbell is an excellent, quick reference.

 

[blue_leaf77]

Usually discussions on the topic of thin film interference only cover the interference aspect of the problem, that is, the fringes formation. I believe you will get more information to solve this problem if you go to any typical topics on Fabry-Perot resonator. Here, one always quantify the transmissivity of the resonator as a function of wavelength, by finding the minima in the transmissivity you can get the maxima in reflectivity in terms of wavelength. Also you will need to know the indices of all the involved media, including the air and water.

 

[jtbell]

You don't need to consider the Fabry-Perot interferometer for this type of problem. The simple thin-film interference equation that applies to this particular situation is sufficient. It would be better if the problem statement clarified whether the light is incident perpendicular to the film, or at some angle. However, I suspect the problem's author was lazy, or else the course/textbook simply has not started to consider non-perpendicular incidence yet.

This looks like a typical thin-film interference problem from a first-year intro physics course, which doesn't usually delve into the theory of the Fabry-Perot interferometer, at least not at most US universities.

 

[Chandra Prayaga]

I believe jtbell is correct, in that an introductory course usually does not deal with a Fabry-Perot, not even with non-perpendicular incidence. The author of the problem can clarify that.

 

[blue_leaf77]

I guess it's a matter of curriculum difference, the way how I was taught thin film problem was that it only dealt with interference due to monochromatic waves, and hence the behavior of transmissivity with respect to wavelength is neglected. But yeah let's hear out from the OP.