In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on θ for constructive interference at P between the ray BP and reflected ray OP

∵PR=d⇒PO=dsec⁡θ and CO=POcos⁡2θ=dsecθcos2θ is Path difference between the two rays Δ=CO+PO=(dsec⁡θ+dsec⁡θcos⁡2θ)Phase difference between the two rays is ϕ = π (One is reflected, while another is direct) Therefore condition for constructive interference should be Δ=λ2,3λ2……or dsecθ(1+cos2θ)=λ2or dcosθ(2cos2θ)=λ2⇒cosθ=λ4d