Consider three equidistant slits A, B, and C (with B located between A and C) illuminated by a monochromatic parallel beam of light. A screen is positioned at a distance D ( D ) such that a point P₀ on the screen is directly opposite to slit A. Let BP₀ - AP₀ = /3 . Determine the intensity at P₀ if the intensity due to any of the three slits individually is I₀ .

Step-by-step solution

Let the distance between adjacent slits be d . The path length from slit A to point P₀ is x_A = D . The path length from slit B to P₀ is x_B = D^2 + d^2 . For D d , the path difference is: x_B = x_B - x_A = D^2 + d^2 - D d^2 2D We are given that x_B = 3 , which implies the phase difference is _B = 2 x_B = 2 3 . The path length from slit C to P₀ is x_C = D^2 + (2d)^2 . The path difference is: x_C = x_C - x_A 4d^2 2D = 4 x_B = 4 3 The phase difference for the wave from C is _C = 2 x_C = 8 3 . Let the amplitude of the