Question

S₁ and S₂ are two coherent sources of radiations separated by distance 100.25 λ, where λ is the wave length of radiation. S₁ leads S₂ in phase by π/2. A and B are two points on the line joining S₁ and S₂ as shown in figure. The ratio of amplitudes of component waves from source S₁ and S₂ at A and B are in ratio 1:2. The ratio of intensity at A to that of B (I_A/I_B) is

(A) ∞

(B) 1/9

(C) 0

(D) 9

Answer 1

Correct option (B) 1/9

Explanation:

For interference at A : S₂ is behind of S₁ by a distance of 100 + λ/4 .(equal to phase difference π/2).

Further S₂ lags S₁ by π/2 . Hence the waves from S₁ and S₂ interfere at A with a phase difference of 200.5π + 0.5π = 201π = π 

Hence the net amplitude at A is 2a – a = a 

For interference at B : S₂ is ahead of S₁ by a distance of 100λ + λ/4 .(equal to phase difference π/2). 

Further S₂ lags S₁ by π/2. 

Hence waves from S₁ and S₂ interfere at B with a phase difference of 200.5π – 0.5π = 200π = 0π. 

Hence the net amplitude at A is 2a + a = 3a 

Hence (I_A/I_B)  = (a/3a)²  = 1/9