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

PR = d Þ PO = d secq  and CO = PO cos 2q =dsecθcos2θPath difference between the two rays D = CO + PO = (d secq + d secq cos 2q)Phase difference between the two rays is f = p (One is reflected, while another is direct) Therefore condition for constructive interference should be Δ=λ2,3λ2...... ⇒dsecθ(1+cos2θ)=λ2 ⇒dcosθ(2cos2θ)=λ2 ⇒cosθ=λ4d