Two-Point Source Interference Pattern

The interference of water waves in a ripple tank. There is destructive interference along the lines marked by Nn (Lines of Nodes) and constructive interference between these lines An(lines of antinodes).

Antinodes (XAn): d2 - d1 = n l; Nodes (XNn): d2 - d1 = (n +1/2)l; n = 0,1,2,3, ...

The waves fronts from S1 and S2 combine at P. Assuming l >> d, such that q is very small (tan q = sin q), and by tan q = x/l, sin q = (d2 - d1)/d [d2 - d1 = nl, for antinodes], we have approximately that

x = n(ll/d) (for antinodes)

and

x = (n + 1/2)(ll/d) ( for nodes).