In Young’s experiment, the ratio of maximum to minimum intensities of the fringe system is 4:1. The amplitudes of the coherent sources are in the ratio

Options

(a) (4:1)
(b) (3:1)
(c) (2:1)
(d) (1:1)

Correct Answer:

(3:1)

Explanation:

I(max) / I(min) = (ɑ₁ + ɑ₂)² / (ɑ₁ – ɑ₂)²

⇒ 4 / 1 = (ɑ₁ + ɑ₂)² / (ɑ₁ – ɑ₂)²

⇒ (ɑ₁ + ɑ₂) / (ɑ₁ – ɑ₂) = 2 / 1

⇒ ɑ₁ + ɑ₂ = 2 (ɑ₁ – ɑ₂)

⇒ 3ɑ₂ = ɑ₁

⇒ ɑ₁ / ɑ₂ = 3 / 1 = 3 : 1