# Wavelength-dependent refractive index

I read in a book about optical fibers that the different spectral components of a light pulse transmitted in the fiber propagate with different velocities due to a wavelength dependent refractive index. Can someone explain that? Why is that silica refractive index depends on the wavelength/frequency of the wave?

The fundamental reason for the wavelength dependance of refractive index ($n$), in fact the fundamental description of refraction itself, is the domain of quantum field theory and is beyond my understanding. Hopefully somebody else can provide an answer on that subject.

However, I can state that it isn't just silica that has a wavelength dependent $n$. In fact, every material has some wavelength dependence, and this property is called dispersion. In optical materials, the dispersion curve is very well approximated by the Sellmeier Equation: $$n^2(\lambda) = 1 + \sum_k \frac{B_k \lambda^2}{\lambda^2 - C_k}$$

usually taken to $k=3$, where $B_k$ and $C_k$ are measured experimentally. As far as I know this equation is not derived from theory; it is completely empirical.

• You can derive the Sellmeier Equation by assuming a set of independent driven harmonic oscillators, yielding the Lorentzian curve (and then use $\omega=2\pi c/\lambda$ and remember that polarization and $n^2$ are linearly connected for non-magnetic materials) – Tobias Kienzler Jan 12 '12 at 15:24

Provided that the electron & the atomic beams also exhibit refraction,it seems that this is a particle's property.Velocity is inversely proportional to particle's mass/size for specific medium.Photon behaves as particle in this effect.Mass is given by de Broglie equation:m=hv/c^2 , v=frequency

• Dear Nikos Binis. It is usually frown upon to directly copy-paste identical answers. (The problem is if everybody start to copy-paste identical answers en mass.) In general in such situations, please consider one of the following options: (i) Delete one of your answers. (ii) Flag for duplicate posts and delete one of your answers. (iii) If you think the three posts are not duplicates, then personalize each answer to address the three different specific questions. – Qmechanic Dec 7 '14 at 16:21