# B Thin film interference - why thin, exactly?

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1. Mar 10, 2017

### FranzDiCoccio

Hi,

in every explanation of thin film interference I came across, little or nothing is said as to why the layer of transparent material creating the effect should be thin.
What would go wrong if that is not the case?
I'm asking because it seems to me that, in principle, the mathematic explanation of the phenomenon would work for (admittedly very ideal) "thick films" too.

What is the point here? Perhaps that a macroscopic layer, however smooth, has "imperfections" on a scale much bigger than the wavelength of the light? I guess that these would spoil any interference.
I think that with careful deposition techniques one could create a very even "macroscopic" layer. That should exhibit the same interference patterns of a thin film, right?

I also thought of light absorption, but I think that this is not a good explanation... After all some macroscopically thick materials are pretty transparent.

Thanks a lot for any insight
Franz

2. Mar 10, 2017

### Grinkle

I don't think there is any deeper understanding to be gained by thinking of films that are more than 1/2 wavelength of light thick may be the reason.

I am not sure, but I think you are right that the interference pattern can occur for thicker films as well at integral multiples of wavelenghts, but its not any different physics.

3. Mar 10, 2017

Besides the need for surface flatness and parallelism, the angle of incidence requirement to get the same interference (e.g. in a bandpass filter) becomes much more stringent if the film becomes much thicker. The film will greatly change its passband of constructive interference with a small change in incident angle if the film is anything but very thin. $\\$ Editing.. Also, spectrally, the interference maxima become much closer together as the material becomes thicker. I believe $\Delta \lambda=\lambda^2/(2nd)$ between the interference peaks. Running a spectral scan and observing these interference peaks becomes very difficult for a sample as thick as $d=1 \, mm$ that has parallel faces. It requires very high a very high resolution spectral measurement to observe the peaks (and valleys) of the transmission spectrum in such a case. (graphing transmission vs. wavelength). Generally thin film filters are made of several layers of the same interference so that the peaks become sharper. They generally will have harmonics(e.g. 2x the frequency which is one half the wavelength) of "pass" wavelengths or spectral regions, but unwanted harmonics can often be blocked with materials that do not pass these unwanted harmonics.

Last edited: Mar 10, 2017
4. Mar 10, 2017

### FranzDiCoccio

Hi Grinkle and Charles,

@ Charles.
Correct me if I'm wrong. You're pointing out that an ideal macroscopic layer would work only for monochromatic light, in the sense that the maxima for the different components of, say, white light would be so close to each other that basically one would see white light anyways.

I'm trying to keep things simple. I'd like to hash out a reasonable and intuitive explanation about what goes wrong with "thick films".
For the sake of simplicity I'd like to limit this to almost zero angle of incidence.

So could I say "in principle one could grow an ideal, macroscopically thick slab and everything would be the same with a monochromatic light, provided that the thickness of the sample is the suitable (possibly very large) integer or half-integer multiple of the wavelength. However, when using white light, the interference maxima of different wavelengths would be so packed together that it would be extremely hard to resolve them".

Does this work?

5. Mar 10, 2017

That is correct (comments about white light), but even with a very monochromatic source, (such as a laser), for a macroscopically thick slab with precisely parallel faces, it could also require very good collimation, i.e. a beam that had one single angle of incidence to observe the interference. There are Fabry-Perot interferometers in use in Optics labs that have a significant distance (perhaps 1/2") between the half-silvered mirrors. It is possible to establish interference with such an apparatus (or a similar one which is a Michelson interferometer) with a monochromatic source. In one experiment we did in college with a (editing this) Michelson interferometer, we used the two lines (5889 and 5996 Angstroms) in the sodium doublet (source was a sodium arc lamp). The source was incident on a diffuser plate so that interference rings (instead of a single bright or reduced intensity across the plane) were observed. By varying the distance between the plates, the ring interference patterns from the 5889 and 5996 lines were made to cycle through each other. From this info, we were able to get a value for the difference between the two wavelengths. This experiment took much effort to align the mirrors=get them parallel so that the interference pattern was centered. In general, experimentation on thin films is far easier. Interference can be observed on macroscopic thicknesses, but the experimental requirements, both spectral (laser lines and even spectral lines from electronic transitions in atoms can work for such interference) and alignment requirements, are much more stringent.

Last edited: Mar 10, 2017
6. Mar 10, 2017

### FranzDiCoccio

Cool example... Yes, I remember doing the same experiment, but that was such a long time ago I did not make the connection. Very helpful, thanks again!

7. Mar 10, 2017

I edited the above=I believe the apparatus we used was a Michelson, but the principles are similar.

8. Mar 10, 2017