4. The full width at half maximum of an atomic absorption line at 589 nm is 100 MHz. A beam of light passes through a gas with an atomic density of

10¹7/m³. Calculate: (a) the peak absorption coefficient due to this absorption line. You can assume that the index of refraction is close to 1 in for this dilute gas; (b) the frequency at which the resonant contribution to the refractive index is at a maximum; (c) the peak value of this resonant contribution to the index of refraction.