As shown in the figure below, a source at S is sending out a spherical wave:

E₁=(A×D/r) cos(wt-2πr/λ); where r is the distance to source S. In addition, there is another plane wave propagating along x axis: E₂=Acos(wt-2πx/λ).

These two waves both projected on a vertical screen as shown in the figure. Please calculate the intensity I along y axis (I should be a function of y, the distance from x axis). D is the distance between the screen and the source.

Hint: For a wave E=E₀cost (wt + q), I = ² = E₀². Also r = .

For k<<1, » 1+k²/2.   cosA+cosB = 2cos[(A+B)/2] cos[(A-B)/2]