Two coherent sources of light with intensities I and 4I produce an interference pattern. At a point P on the screen, the path difference between the interfering waves is 4 . At another point Q , the resultant intensity is greater than the resultant intensity at P by 2I . If the phase difference between the waves at Q is N , the value of N is _____.

Step-by-step solution

The phase difference at point P is related to the path difference by: _P = 2 x = 2 4 = 2 The resultant intensity at P is given by the interference formula: I_P = I₁ + I₂ + 2 I₁ I₂ ( _P) I_P = I + 4I + 2 I 4I ( 2 ) I_P = 5I + 4I(0) = 5I It is given that the intensity at Q is I_Q = I_P + 2I . I_Q = 5I + 2I = 7I Now, applying the intensity formula for point Q : I_Q = I + 4I + 2 I 4I ( _Q) 7I = 5I + 4I ( _Q) 2I = 4I ( _Q) ( _Q) = 1 2 This gives the phase difference at Q as _Q = 3 . Comparing this with the given phase d