About Scott Valentine Expertise I can address general physics, with some specifics on nuclear and astrophysics, thin films, magnetism, optics, and materials physics (solid state, etc). Recent work includes high pressure gasses and solid state diffusion. I tend not to answer math questions, but instead focus on concepts and understanding.
Experience I currently work at a national laboratory, performing a wide range of engineering and basic science tasks. Previous experience includes thin film deposition and magnetoresistance studies for use in recording and sensing devices.
Question Why is it that the Bragg diffraction law does not contain a refractive index parameter? Path length is just geometrical not optical.
Answer Hi Anne Marie,
Great question!
Bragg diffraction has to do with wave interactions on crystal structure, specifically in plane spacing. By contrast, refractive index refers to changes in phase velocity of the waveform due to electric field interactions at the atomic level.
As you mention, path length is the important consideration for Bragg diffraction. But for diffraction to 'work', there must be some kind of ordered system. Otherwise, the random scattering would destroy any pattern. Thus you can not use Bragg's laws for liquids. Also, Bragg seeks to describe the environment in a single material by interrogating the surface, which presumes a wave coming in uninterrupted, interacting, then leaving uninterrupted. The surface is important, but not the interface as the wave is reflected.
Refractive index can be performed on liquids, and may also be anisotropic for some materials. It is a comparison of phase velocity in a medium and the velocity in a vacuum, and does consider interfaces rather than surfaces. Phase velocity changes as the incoming wave's electric field interacts with the atoms of a material, which causes a sort-of sympathetic wave of the same frequency, but delayed in phase. When combined, the resultant wave has the same frequency but shorter wavelength, so the phase velocity is slowed.
Now, back to your question... Bragg's law ignores refractive index because they result from largely unrelated phenomena. If Bragg were to consider RI, the implication would be that the diffraction pattern would change based on the change in phase velocity. But Bragg looks at reflection of waves, and the interaction of the resulting differences in path length, while refractive index, in this context, would look at the change in angle with respect to the incident beam and the surface. This would have little to no effect on the pattern at the detector, except perhaps in placement, which in turn would be negligible.
In turn, RI ignores path length altogether, as the phase interactions are occurring at the wavelength level and have nothing to do with reflections from interatomic spacing.
I hope this helps! If you have further questions, please feel free to ask or follow up =)
