The correct option is B λ2π(ϕ+π2)
Given ,
y1=a1sin(ω t−2π xλ) ........(1)
and
y2=a2cos(ω t−2π xλ+ϕ)=a2sin(ω t−2π xλ+ϕ+π2) ........(2)
From (1) and (2),
Phase difference Δϕ=ϕ+π2
Since, Phase difference (Δϕ)=2πλ× Path difference (Δx)
Δx=λ2π×Δϕ ⇒Δx=λ2π(ϕ+π2)
Thus, option (b) is the correct answer.