Derive relation between refractive index and wave length of light
Answers
Answered by
2
In general these are not really connected, however refractive index is usually slightly different for different wavelengths. This is called chromatic dispersion. Here is the short version of a long story…
At the atomic scale, the negatively charged electrons orbit the positively charge nuclei and essentially form electron clouds around the nuclei. When an electric field is applied to this material, the electron clouds and the nuclei are pushed in opposite directions and the electron clouds stretch. When the electrons are offset from their equilibrium position, the material is said to be polarized. This is a resonant system that can be compared to a mass on a spring. When the applied electric field is removed, the electron clouds return to their equilibrium positions, but ring for a short time. It is possible to write the equation of motion for a mass on a spring, but the the restoring force of the spring is the electrostatic attraction of the electron and nucleus and the mass is the mass of the electron. This equation can be manipulated and averaged over millions of atoms to give an overall material response. This is called the Lorentz oscillator model and is written as
ϵr(ω)=1+ω2pω20−ω2−iωΓ
In this equation, ω is the angular frequency, ωp is the plasma frequency, ω0 is the resonant frequency, and Γ is the damping rate. Given the complex dielectric constant above, the complex refractive index is
n(ω)=ϵr(ω)−−−−√
At the atomic scale, the negatively charged electrons orbit the positively charge nuclei and essentially form electron clouds around the nuclei. When an electric field is applied to this material, the electron clouds and the nuclei are pushed in opposite directions and the electron clouds stretch. When the electrons are offset from their equilibrium position, the material is said to be polarized. This is a resonant system that can be compared to a mass on a spring. When the applied electric field is removed, the electron clouds return to their equilibrium positions, but ring for a short time. It is possible to write the equation of motion for a mass on a spring, but the the restoring force of the spring is the electrostatic attraction of the electron and nucleus and the mass is the mass of the electron. This equation can be manipulated and averaged over millions of atoms to give an overall material response. This is called the Lorentz oscillator model and is written as
ϵr(ω)=1+ω2pω20−ω2−iωΓ
In this equation, ω is the angular frequency, ωp is the plasma frequency, ω0 is the resonant frequency, and Γ is the damping rate. Given the complex dielectric constant above, the complex refractive index is
n(ω)=ϵr(ω)−−−−√
Similar questions