A linearly polarized plane wave of wavelength lembda, is travelling in air and ia incident normally on a plane sheet of glass. Show that the ratio of the reflected to the incident electric field amplitude is (n(glass)-n(air))/(n(glass)+n(air)) where n(air) and n(glass) are the refractive indices of air and glass respectively.

The glass sheet is now coated on the incident side with a material with a refractive index n(coat) = √((n(air)*n(glass))) and a thickness d = λ/4. Prove that there is now, in principle, no reflected power.