The phase difference Δϕ is related to the path difference Δx by the relation Δϕ=λ2πΔx.
For point A, the path difference is ΔxA=3λ.
ΔϕA=λ2π×3λ=32π
The intensity at point A is given by IA=Imaxcos2(2ΔϕA).
IA=Imaxcos2(3π)=Imax(21)2=4Imax
For point B, the path difference is ΔxB=6λ.
ΔϕB=λ2π×6λ=3π
The intensity at point B is given by IB=Imaxcos2(2ΔϕB).
IB=Imaxcos2(6π)=Imax(23)2=43Imax
The ratio of intensities at points A and B is:
IBIA=43Imax4Imax=31
Answer: 1/3