# Index of Refraction and Sellmeier’s Equation

Now that we know how the classical dipole behave, we can solve the equation of motion for the macroscopic polarization density, given as:

$$\frac{d^2P}{dt^2}+(\gamma + \frac{2}{T_2′})\frac{dP}{dt}+\omega_0^2P = \frac{Ne^2}{m}E$$

which we found using our heuristic model of the polarization.