In an interference pattern produced by two coherent sources of light, the ratio of the difference between the maximum and minimum intensities to their sum is given as 24 25 . The ratio of the maximum amplitude to the minimum amplitude in this interference pattern is

Step-by-step solution

Let the intensities of the two sources be I₁ and I₂ , and their respective amplitudes be A₁ and A₂ . The maximum and minimum intensities are given by: I_ = (A₁ + A₂)^2 I_ = (A₁ - A₂)^2 We are given the ratio: I_ - I_ I_ + I_ = 24 25 Substituting the expressions for I_ and I_ : (A₁ + A₂)^2 - (A₁ - A₂)^2 (A₁ + A₂)^2 + (A₁ - A₂)^2 = 24 25 Simplifying the numerator and denominator: 4A₁ A₂ 2(A₁^2 + A₂^2) = 24 25 2A₁ A₂ A₁^2 + A₂^2 = 24 25 Let the ratio of amplitudes be y = A₁ A₂ . Dividing the numerator and denominator