In a Young\'s experiment, the paths from the slits to a point on the screen diff

Question

In a Young's experiment, the paths from the slits to a point on the screen differ in length causing destructive interference at the point. Which of the following path difference would cause this destructive interference?
a) 5/2

b) 3/4

c) 4

d) none of the above

I understand that if the light from one of the slits has a wavelength that falls behind a half a wave then there will be destructive interference hence (5/2 is the answer); however, I am unable to visualize 3/4 being constructive interference. If anyone could guide me on how to visualize this, I would greatly appreciate it.

Explanation / Answer

The path difference and phase difference is related by the equation phase difference = 2/ (path difference) = (2/ )(3/4)     = 6 condition for constructive interference : When constructive interference occurs at a point , the resultant intensity at thatn point is maximum . The intensity will maximum by relation I = 4I0cos2 /2 hence cos /2 = ±1 /2 = 0, 2 , 3 = 0, 4 , 6, = n(2) so our phase difference 6 will make constructive interference.

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