Two coherent sources with different intensities emit waves that interfere with each other. If the ratio of the maximum intensity to the minimum intensity is 25 , the ratio of the intensities of the two sources is

Step-by-step solution

Let the intensities of the two coherent sources be I₁ and I₂ . The maximum intensity in the interference pattern is given by I_ max = ( I₁ + I₂ )^2 The minimum intensity is given by I_ min = ( I₁ - I₂ )^2 Given that the ratio of maximum to minimum intensity is 25 : I_ max I_ min = ( I₁ + I₂ )^2 ( I₁ - I₂ )^2 = 25 Taking the square root on both sides: I₁ + I₂ I₁ - I₂ = 5 I₁ + I₂ = 5 I₁ - 5 I₂ 6 I₂ = 4 I₁ I₁ I₂ = 6 4 = 3 2 Squaring both sides, the ratio of the intensities is: I₁ I₂ = 9 4