First slide
Coherent sources and their importance in interference
Question

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 
 

Difficult
Solution

PR=dPO=dsecθ and CO=POcos2θ=dsecθcos2θ is
 

Path difference between the two rays 
Δ=CO+PO=(dsecθ+dsecθcos2θ)
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)=λ2
or dcosθ(2cos2θ)=λ2cosθ=λ4d

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