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. The intensity will be maximum when `f = 2 np,` the sources are in same phase.
Thus `I_(max) I_(1) + I_(2) + 2 sqrt(I_(1) I_(2)) = ( sqrt I_(1) + sqrt I_(2))^(2)`
Similarly, for n indentical waves,
`I_(max) = (sqrt I_(0) + sqrt I_(0) + ....)^(2) = n^(2) I_(0)`
b. The incoherent sources have phase difference that varies randomly with time.
Thus, `[cos phi]_(av) = 0`
Hence, `I = I_(2) + I_(2)`
Hence, for n idental waves, `I = I_(0) + I_(0) + ... = n I_(0)`