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 8. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by Ei = Eoiû Re [exp j(kr - wt + 8;)]. From this, prove that the total intensity Inet including interference is given by Inet = |Ec|2 270 where the complex amplitude Ę is defined by N Ec = Eoi exp(jdi), and no is the impedance of free space. i=1

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 8. Therefore the ith wave (for 1 ≤ i ≤N) has electric field given by Ei = Eoiû Re [exp j(kr - wt + 8;)]. From this, prove that the total intensity Inet including interference is given by Inet = |Ec|2 270 where the complex amplitude Ę is defined by N Ec = Eoi exp(jdi), and no is the impedance of free space. i=1