Glass silvering phenomena and further studies upon reflective layers

[m0022l]

I was working on this college project in optics, and I was thinking of ways to preserve light by multiple reflections. The question is, if I manage to coat a transparent glass (or acrylic) rod with a reflective layer (via silvering), will the internal layer of the rod be reflective as well or just the outside? In more words, when propagating a beam inside the rod; will it reflect as a result of silvering?

 

[turbo]

Have you studied front-surface silvering?

 

[tadchem]

Fermat's Principle and Snell's Law (the same thing, really) dictate that you can only get total internal reflection if the refractive index on the outside of the rod's surface is LOWER than the index on the inside.
http://en.wikipedia.org/wiki/Total_internal_reflection#Critical_angle

 

[Khashishi]

Metals have complex indices of refraction and the mechanism for reflection is somewhat different than for dielectrics. Short answer, yes, coating the rod will increase the reflectivity. This is essentially what a mirror is--a piece of glass with silver painted on the back. But at some steep angle of incidence, the silver layer won't really do any good because you already have total internal reflection. I don't know how total internal reflection works for a complex refractive index.

 

[tadchem]

Metals have complex indices of refraction and the mechanism for reflection is somewhat different than for dielectrics. Short answer, yes, coating the rod will increase the reflectivity. This is essentially what a mirror is--a piece of glass with silver painted on the back. But at some steep angle of incidence, the silver layer won't really do any good because you already have total internal reflection. I don't know how total internal reflection works for a complex refractive index.

Reflection of visible light at the interface between the glass rod and the metal in NOT total internal reflection. That can only occur when moving from an optically denser medium into a less dense one (i.e., n1 > n2).

Wiki has a nice little blurb on the Complex Index of Refraction.

Lorentz developed the theory. Briefly, all materials have complex indices of refraction at all wavelengths. The real part of the refractive index represents the phase speed, while the imaginary part indicates the amount of absorption loss when the electromagnetic wave propagates through the material (classically called the 'extinction coefficient). The extinction coefficient may be near 0 for materials nearly transparent to a given wavelength.

The theory nicely explains absorption bands in dense materials, dispersion, refraction, reflection, and even 'negative' refractivity (n <1.000) wherein light appears to move faster than c. The shape of the absorption curve as a function of wavelength / frequency is referred to as a Lorentzian curve.