Question

The intensity at the central maximum (O) in a Young’s double slit experimental set-up shown in the figure is I_O. If the distance OP equals one-third of the fringe width of the pattern, show that the intensity at point P, would equal `(I_0)/4`.

Answer 1

Intensity at the central maxima = I₀ 

Distance OP is one-third of the fringe width, ` x = 1/3 beta ` (given)

Fringe width is given by`(lambdaD)/d`

`therefore    x= (lambda D)/(3d)`

Path difference , ` DeltaP = (xd)/D` and , 

Phase difference, `phi = (2 pi) / lambda ( Delta P)`

                                  `= 2 pi /3`

Intensity at point P , I = ` I _0 cos^2  phi/2`    

                                 ` = I_0 cos^2  ((2pi)/3) = I_0/4`