What happens to Snell's Law when considering the atomic properties of materials?

[eminent_youtom]

Violation of Snell's Law??

Let's pass a beam of photon with low intensity towards a smooth surface. If the beam has infinitesimal thickness and passes through the gap of atoms, does it follow Snell's Law?
What are the restriction and limitation of Snell's Law?
your answer will be appreciated.

 

[Troels]

Let's pass a beam of photon with low intensity towards a smooth surface. If the beam has infinitesimal thickness and passes through the gap of atoms, does it follow Snell's Law?

First, let us consider the problem in the continuum hypothesis, ie. no atoms. In this case yes; Snells law can be derived using the ray optics model and triangular calculations, but it can also be derived using advanced wave mechanics and electrodymanic boundary conditions, which make no assumptions on the spatial extention of the wave.

In case of a wave of short wavelength, the atomic properties of the material begins to be important. In this case, you wil have to consider the transmission and reflection as a scattering process from a regular latrice. Here braggs law give you the angels. It is, I suppose, if your latrice is completely regular, possible to make a photon of very short wavelength travel through a latrice channel without interacting with the electrons.

 

[eminent_youtom]

First, let us consider the problem in the continuum hypothesis, ie. no atoms. In this case yes; Snells law can be derived using the ray optics model and triangular calculations, but it can also be derived using advanced wave mechanics and electrodymanic boundary conditions, which make no assumptions on the spatial extention of the wave.

In case of a wave of short wavelength, the atomic properties of the material begins to be important. In this case, you wil have to consider the transmission and reflection as a scattering process from a regular latrice. .

Thank you for your reply.
Its bit tough for me to understand. what does the atomic properties of the material begins to be important means? and how does snell's law hold on my question?