A monochromatic light source of wavelength λ is placed at S. Three slits S₁, S₂ and S₃, the source S, and the point P are arranged as shown in the figure. If S₁P - S₂P = λ/6 and S₁P - S₃P = 2λ/3, and I is the intensity at P when only one slit is open, find the intensity at P when all three slits are open.

Question

G1 Physics · Accepted Answer

Because S and P are symmetrically placed at equal horizontal distance D from the slit plane, for each slit Sᵢ we have SSᵢ=SᵢP. Therefore the total optical path through slit Sᵢ is 2SᵢP. Given S₁P-S₂P=λ/6, the total path difference between the waves through S₁ and S₂ is 2(λ/6)=λ/3, so their phase difference is 2π/3. Also S₁P-S₃P=2λ/3, so the total path difference between S₁ and S₃ is 4λ/3, which is equivalent to λ/3 modulo λ. Thus the S₂ and S₃ waves are in phase, while the S₁ wave differs from t…