Question

The two coherent sources of intensity ratio β produce interference. The fringe visibility will be ______. 

(A) 2 β (B) (β/2) (C) {√β / (1 + β)} (D) {(2√β) / (1 + β)}

Answer 1

The correct option is (D) {(2√β) / (1 + β)}.

Explanation:

(I₁ / I₂) = (β/1)   …. given

Intensity ∝ (amplitude)² hence

(a₁ / a₂) = √(I₁ / I₂) = √(β/1)

[(I_max) / (I_min)] = [(a₁ + a₂)² / (a₁ – a₂)²]     hence

[(I_max) / (I_min)] = [(√β + 1)² / (√β – 1)²]  .......(1)

Fringe visibility is given by V = [(I_max – I_min) / (I_max + I_min)]

 From (1)

V = [{(√β + 1)² – (√β – 1)²} / {(√β + 1)² + (√β – 1)²}]

= [{(β + 2√β + 1) – (β – 2√β + 1)} / {(β + 2√β + 1) + (β – 2√β + 1)}]

= [(4√β) / {2(β + 1)}]

= {(2√β) / (β + 1)}