Two beams of light having intensities I and 4 I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π 2 and π 3 at points A and B respectively. The difference between the resultant intensities at the two points is x I . The value of x will be _____ .

Step-by-step solution

Given here, phase difference at point A and B are ϕ A = π 2 and ϕ B = π 3 . Resultant intensity at point A , I A = I + 4 I + 2 I 4 I cos π 2 ⇒ I A = 5 I + 4 I 0 = 5 I Resultant intensity at point B , I B = I + 4 I + 2 I 4 I cos 60 ° = 5 I + 4 I × 1 2 = 7 I Difference in intensities is I B - I A = 7 I - 5 I = 2 I . Thus, value of x = 2 .