91Ó°ÊÓ

As shown in the figure the phasor diagrams, for an 8-slits interference pattern, for $\mathrm{Ï•}=\frac{3\mathrm{Ï€}}{4},\frac{\mathrm{Ï€}}{4},\frac{3\mathrm{Ï€}}{4},\mathrm{and}\frac{7\mathrm{Ï€}}{4}$, and respectively. We see that the phasor diagram for $\mathrm{Ï•}=\frac{\mathrm{Ï€}}{4}$is the same as for role="math" localid="1663903941522" $\mathrm{Ï•}=\frac{7\mathrm{Ï€}}{4}$except that the direction of rotation is reversed.

The same goes for the phasor diagram for role="math" localid="1663903966954" $\mathrm{Ï•}=\frac{3\mathrm{Ï€}}{2}$and$\mathrm{Ï•}=\frac{\mathrm{Ï€}}{2}$ .

In each of the four cases, the resultant phasor is zero, and the intensity is zero.

We observe the following. In case $\mathrm{Ï•}=\frac{3\mathrm{Ï€}}{4},\frac{\mathrm{Ï€}}{4},\frac{7\mathrm{Ï€}}{4}$, there is destructive interference for each of the following pairs of slits: (1,5), (2,6),(3,7), and (4,8). In case $\mathrm{Ï•}=\frac{3\mathrm{Ï€}}{2}$, each of the following pairs of slits cancels each other : (1,3 or 7),(2,4 or 8), (5,3 or 7), (6,4 or 8).