# Question regarding thin film interference

1. Jul 15, 2008

### ugresearcher

My question concerns thin films of varying thickness. I have a basic understanding of thin film interference, and understand the effects of thickness on wavelength, and that with increasing thickness color fringes will be evident. I understand that the color fringes come from:
n*t = m*$$\lambda$$
where n is the index of refraction, t is the film thickness, and m is an integer greater than zero.

My question deals with how the fringes overlap. For example say at some point with some thickness there is a wavelength outside the visible spectrum of 1200nm; using m = 2 and m = 3 would both allow for the wavelength to be in the visible spectrum at 2 different colors.

Upon observing this (assuming the observer is perpendicular to the film) how would the color look? Is there some type of rule for blending these two colors together? I have noticed that as there is increasing thickness the color fringes increase in overlap until they go gray.

Any help would be appreciated, and thanks for reading!

2. Jul 15, 2008

### Andy Resnick

I'm not sure I understand your question- are you asking how the wavelength will change with interference order? (It won't).

Thicker films may satisfy multiple wavelengths simultaneously: both order (m) and dispersion (n is a function of wavelength) may consipre to allow multiple wavelengths interfere at the same time, but illuminating a film with monochromatic light will not ever give you light at a different wavelength (assuming passive linear materials).

3. Jul 16, 2008

### ugresearcher

I'm sorry about how i worded this, I'm an engineer and not a physicist so this stuff isn't native to me.

My issue is what an observer would see (i.e. what color) when there are multiple wavelengths that interfere at one point if the film is illuminated with white light.

4. Jul 16, 2008

### Andy Resnick

Oh... that's a very interesting and difficult question! It's fairly easy to write down the emergent spectrum- start with the source and subtract out the reflection bands- but that doesn't exactly tell you what you would *see*, since the eye is a strange detector. Even replacing the eye with a camera isn't so simple- a 3-chip color camera and a camera with a Bayer filter can give different colors.

For the sake of argument, let's start with sunlight incident on a filter that reflects both 500 nm and 600 nm light. The bandwidth of reflectivity can be made very small. The light incident on your eye is then what normally is incident, less 500 nm and 600 nm. What color is that? More precisely, what *percieved* color is that? For that matter, what color is 500 nm plus 600 nm? It ultimately depends on the detector.

There are several ASTM volumes regarding color and light, and a lot of them are there because it's not so simple to say what color something has- the color brown, for example. Or a pastel blue. Those are not simple colors in the physical sense, but they are perfectly well-defined in other ways (color space, for example). Add in surface effects (gloss, textured) or interference effects (iridescence, etc.) and things get very confusing very quickly.

5. Jul 16, 2008

### ugresearcher

Hmm...maybe it would be of some aid if I elaborated on my situation further.

I am trying to simulate the evaporation of a fluid on a flat mirror plate. As the fluid evaporates (which it does non-uniformly as the plate is removed from the bath) there are colors observed on the plate. In simulating this, I would like to show the exact same colors using my data for film thickness. I know that color fringes will form, but with increasing thickness there are multiple wavelengths which satisfy a thickness.

I'm just in need of an easy way to determine the color at these points, it's been difficult for me as an engineer so far.

6. Jul 16, 2008

### Andy Resnick

Oh, ok- now I'm with you. I was involved in a similar project while at NASA (Constrained Vapor Bubble project). Interesting signature- you involved with any microgravity work?

I'd say the easiest way to simplify this is to use monochromatic light- and make the experimental guys use monochromatic light. That will make your life infinitely easier.

The data is probably only really valid for first-order interference (the really thin part of the film). Talk to the folks who took the data, see if you can get some details on how they interperet the results.

7. Jul 17, 2008

### ugresearcher

Well I don't know if it's possible for them to use monochromatic light. The only data we were provided with were a few movies of these things coming out of the bath, all the film thickness data we have is from simulations, I'd just like to have the plots match up with the videos. I figured attempting to do this would not be as trivial as I thought. I think I'm going to just start playing around with things and maybe average or rms average the wavelengths that satisfy multiple conditions to see if it looks pretty (since that's all I'm going for, I mean we know our simulations work, but showing them to some people alongside the video and having the simulation match up would prove it to them quite easily).

To go off topic a little, I still don't have my BS. I'm going for Mechanical Engineering, and although I've worked on 3 different research projects, I've never done any microgravity stuff.