hey there,
● Answer -
∆x = λ(θ+π/2)/2π
● Explanation -
Given wave eqns are,
y1 = a1sin(ωt-2πx/λ) ...(1)
y2 = a2cos(ωt-2πx/λ+θ)
y2 = a2sin(ωt-2πx/λ+θ+π/2) ...(2)
Comparing (1) & (2), phase difference is
∆θ = θ+π/2
Path difference is given by -
∆x = ∆θ × λ / 2π
∆x = λ(θ+π/2)/2π
Hence, path difference is λ(θ+π/2)/2π .
Thanks for asking...