Consider the arrangement shown in figure (17-E7). By some mechanism, the separation between the slits S 3 and S 4 can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S 1 S 2 and S 3 S 4 . When , the intensity measured at P is I. Find this intensity when z is equal to

Consider the arrangement shown in figure (17-E7). By some mechanism, the separation between the slits S₃ and S₄ can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S₁S₂ and S₃S₄. When , the intensity measured at P is I. Find this intensity when z is equal to

Let the intensity of slits and be . For and , The distance from the central maximum is .

So the path difference is

Given,

And the corresponding phase difference is

Now, intensity at each slit is given by

Here, P is also central maxima. So the intensity is

(a)For ,

and

Therefore, intensity at each slit is

.

This means that both slits and would be dark. Thus intensity at P would be zero.

(b)For ,

and

Therefore, intensity at each slit is

.

Hence intensity at P is

(c)For ,

and

Therefore, intensity at each slit is

.

Hence intensity at P is

1