# Refraction Index vs. Material Thickness

1. Nov 9, 2005

### jvicens

Take a beam of monochromatic light pointed at a sheet of quartz 2" thick. The beam is striking the surface of the quartz at a fixed angle different than zero. Part of the beam will be reflected and another part of the beam will be refracted. Its exact path through the sheet will depend on the refraction index of the quartz and the refraction index of the first media.
Question: What is the minimum thickness this sheet of quartz must have to conserve the same refraction index of the original 2" thick quartz sheet? I suppose there is a minimum of material below which it makes no sense talking about refraction index or about any other material property. Would this limit be 2 layers of atoms, or three or maybe 100 layers? What does it depend on?

2. Nov 9, 2005

### Pieter Kuiper

I do not think this is a very good question. Also thin layers have a well-defined refractive index. For example, anti-reflection-coating that are a quarter of a wavelength thick.

At two layers, all atoms are surface atoms, in a different chemical bonding state. Of course, that has different optical properties.

3. Nov 9, 2005

### jvicens

This is exactly the point and the reason for my question. If you start taking layers of atoms off from that reflective coating one after another, how many can you leave untouched before the refractive index changes and the beam of light refracts with a different angle?

4. Nov 9, 2005

### armandowww

don't forget classical subject

I think your doubt is unmotivated at an atomic level.
The only limit you have to involve about Snell refractive law is the diffraction limit, that occurs when light wavelength is of the order of your real obstacles.
red light wavelenght = 0.6 micrometers ==> diffraction on CD's pinholes
X-Ray wl = 0.1 nanometers ==> Bragg diffraction on crystal lattice sites

On a common point of view (i.e. surfaces of your glasseseye chemically worked), the lowest point of thickness of high (or anti) reflective coating never get down under tens of micrometers.

5. Nov 9, 2005

### Renge Ishyo

From my understanding, the thickness of the material does not affect the index of refraction at all no matter how thin you make it (so long as you still have material present that can be identified as quartz, it should bend the same amount at the interface). The thickness seems to alter only the location with which light exits the material. For example, if you shine a light on a sheet of quarts 1cm thick at a slight angle, it will bend briefly while in the material, and then exit the material on the other side at a slightly lower point than that with which it entered (assuming that the two sides of your material are parallel to one another, it will exit the material at the same angle you started with). If you did the same experiment with a sheet of quartz 10 cm thick and used the same slight angle, the light will bend for longer in the material and will exit further down on this sheet (again, if the sheet was parallel, it will exit with the same angle you started with).

That's my understanding of the phenomenon at least. I suppose if you made the sheet really thin there would be no perceptible displacement downward if you do the same experiment, but then again, once you start peeling away at the atomic structure you'll end up removing quartz (and yeah, when quartz is no longer present in it's crystalized form, then at that point the light will refract differently...but that is probably because "quartz" is no longer there).

6. Nov 9, 2005

### ZapperZ

Staff Emeritus
No sure why this is an issue. For transparent dielectric thin film, the refractive index is a function of thickness. See, for example a review (and an old one too) by O.S. Heavens, Rep. Prog. Phys. v.23, p.1 (1960).

Zz.

7. Nov 9, 2005

### dlgoff

I don't have access to Rep. Prog. Phys. Is there a simple equation for refractive index as a function of thickness?

Thanks

8. Nov 9, 2005

### ZapperZ

Staff Emeritus
I don't have the reference with me at home. So you'll have to wait till I get to work tomorrow. However, from what I can remember, there is no simple analytic expression for the index of refraction of a dielectric thin film as a function of thickness. This is because for very thin film, it must be fabricated on a substrate. In such a study, the substrate should be transparent, but still with an index of refraction of its own. So this must be taken into account in any experimental measurement.

I don't remember the purely theoretical derivation, if any, in that paper.

Zz.

9. Nov 10, 2005

### Dr Transport

Check out effective medium theory, it is useful in this case.......