Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is / 2 at point P and at point Q on the screen. The difference between the resultant intensities at points P and Q is ( 90^ =0, =-1 )

Step-by-step solution

The interference of two light sources with intensities I₁ and I₂ and phase difference produces a resultant intensity given by I_R = I₁ + I₂ + 2 I₁ I₂ . With I₁ = I and I₂ = 9I , the resultant at point P where _P = 2 is I_P = I + 9I + 2 I 9I 2 = 10I since 2 = 0 . At point Q where _Q = , = -1 , so I_Q = I + 9I + 2 I 9I (-1) = 10I - 6I = 4I . The difference in intensities is I_P - I_Q = 10I - 4I = 6I .