Question

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio

(a) 25 : 1

(b) 5 : 1

(c) 9 : 4

(d) 625: 1.

Answer 1

The correct answer is (c) 9 : 4

EXPLANATION:

Since the resultant field at a point is given as

E₀² = E₁² + E₂² + 2E₁E₂ cosδ

Where E₁ and E₂ = amplitudes of interfering waves and δ is phase difference. For maximum amplitude cosδ= 1 and for the minimum cosδ = -1, hence maximum amplitude is given as

E₀² = (E₁ + E₂)² and the minimum amplitude as E₀'² = (E₁ - E₂)²

Since the intensity is proportional to the square of the amplitude, hence the maximum intensity

I = (√I₁ + √I₂)² and the minimum intensity

I' = (√I₁ - √I₂)²

Let I₁ = k I₂

Hence, I = (√k+1)² I₂ and I' = (√k - 1)² I₂

Given, I/I' = 25

→(√k+1)²/(√k-1)² = 25

→√k + 1 = 5√k - 5

→4√k = 6

→√k =6/4 = 3/2

→k = 9/4

Hence the intensities of the sources are in the ratio

9:4.