Consider a plane electromagnetic wave E(z,t) = Ege'**~\" y that is perpen- diculary incident on a slab of dilute gas located at = = 0 with thickness A-:. a) Model each gas molecule as having a single electron in a simple harmonic oscillator potential with natural frequency wy. Calculate the amplitude of the forced oscillations from the incident electromagnetic field. b) Find the total field from the radiation of the forced oscillations at a point located at positive z > A You will need to perform an integral and deal with a term at infinity. Assume that there are n molecules per unit area in the slab, and that z is large enough so that all charges in the slice are appoximately perpendicular to the line of sight. ) Assume that the incident wave is essentially undiminished, so that at the observation point z the field is the superposition of the incident wave E(z,t) = Epe'**~\"! plus that of the radiation you calculated in part b). Compare this to field expected expected if you treated the slab as having an index of refraction , and use your result to find the index of refraction of the gas as a function of the parameters in the