Find the maxinum intensity in case of interference of n identical waves each of intensity `I_(0)` if the interference is
(a) coherent and (b) incoherent.

Explanation

The resultant intensity is given by
`I=I_(1)+I_(2)+2 sqrt(I_(1)I_(2))cos phi`
(a) The sources are said to be coherent if they have constant phase difference between them. Then intensity will be maximum when `phi = 2n pi`, the sources are in same phase.
Thus `I_("max")=I_(1)+I_(2)+2sqrt(l_(1)l_(2))`
`=(sqrt(l_(1))+sqrt(l_(2)))^(2)`
Similarly, for n identical waves,
`I_("max")=(sqrt(l_(0))+sqrt(l_(0))+....)^(2)=n^(2)l_(0)`
(b) The incoherent sources have phase difference that varies randomly with time Thus `[cos phi]_(av)=0`
Hence `I=I_(1)+I_(2)`
Hence for n identical waves,
`I=I_(0)+I_(0)+............ = nI_(0)`