99 Percentile Qs Bank for JEE MainPhysicsWave Optics
In the adjacent diagram, CP represents a wavefront and AO   &   BP , the corresponding two rays. Find the condition of θ for constructive interference at P between the ray BP and reflected ray OP .
Options
- Acos θ = 3 λ 2 d
- Bcos θ = λ 4 d
- Csec θ - cos θ = λ d
- Dsec θ - cos θ = 4 λ d
Correct answer
B. cos θ = λ 4 d
Step-by-step solution
P R = d   ∴  P O = d sec θ and C O = P O cos 2 θ = d sec θ cos 2 θ   Path difference between the two rays is, Δ x = P O + O C  = d sec θ + d sec θ cos 2 θ phase difference between the two rays is Δ ϕ = π   oneisreflected , whileanotheris direct Therefore, condition for constructive interference should be Δ x = λ 2 , 3 λ 2 ...... or, d sec θ 1 + cos 2 θ = λ 2 or, d cos θ 2 cos 2 θ = λ 2