A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eoi and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by Ei = Eoiû Re [expj(k-r-wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec² Inet 270 where the complex amplitude E, is defined by Ec=Eoi exp(jói), i=1 and is the impedance of free space.

A number N of plane waves are travelling parallel; the waves share a common wavevector k and common direction of electric field vector along unit vector û, but each wave has its own distinct amplitude Eoi and phase difference &;. Therefore the ith wave (for 1 ≤ i ≤ N) has electric field given by Ei = Eoiû Re [expj(k-r-wt+d;)]. From this, prove that the total intensity Inet including interference is given by Ec² Inet 270 where the complex amplitude E, is defined by Ec=Eoi exp(jói), i=1 and is the impedance of free space.