Two sources of intensity I and 4I are used in an interference experiment. Find the intensity at points where the waves from two sources superimpose with a phase difference
(i) zero (ii) `(pi)/(2)` and (iii) `pi`.

Explanation

The resultant intensity at a point where phase difference is `phi` is
`I_(R) = I_(1) + I_(2) + 2sqrt(I_(1)I_(2)) cos phi`
As `I_(1) +I and I_(2) = 4I therefore`
`I_(R) = I + 4I + 2sqrt(I.14) cos phi`
`I_(R) = 5I + 4I cos phi`
(i) When `phi = 0 : I_(R) = 5I + 4I cos 0 = 9I`
(ii) When `phi = (pi)/(2) , I_(R) = 5I + 4I cos (pi)/(2) = 5I`
(iii) When `phi = pi , I_(R) = 5I + 4I cos pi = 5I - 4I = I`
`phi = 0 , I_(R) = 9I`
`phi = (pi)/(2) , I_(R) = 5I`
`phi = pi , I_(R) = I`