An interference is observed due to two coherent sources, A and B, separated by a distance 4 along the Y-axis, where is the wavelength of the source. A detector D is moved along the positive X-axis. The number of points on the X-axis, excluding x = 0 and x , at which maxima will be observed, is

Step-by-step solution

Let source B be at (0,0) and source A be at (0, 4 ) . The path difference p at a point D(x, 0) on the positive X-axis is given by: p = AD - BD = x^2 + (4 )^2 - x Let us check the boundary values of the path difference: At x = 0 , p = 0 + 16 ^2 - 0 = 4 . As x , p = _ x x (1 + 16 ^2 x^2 )^ 1/2 - x = 0 . For constructive interference (maxima), the path difference must be an integer multiple of the wavelength: p = n Since the points x = 0 and x are explicitly excluded, the path difference must strictly lie in the range