Physics - Interference Pattern

In order to form a constructive interference, the path difference between waves from the two sources must at least equal to one wavelength w .

Since path difference = a.sin(theta)
where a is the separation between the two sources,
angle (theta) is the angular position of the bright fringe, where constructive interference occurs,

when a = w/2, path difference = (w/2).sin(theta). The largest value of sin(theta) equals to one, thus max value of path difference = w/2, which is shorter than a wavelength. Therefore, no constructive interference would occur.