Two coherent light waves having an intensity ratio of 4:1 produce an interference pattern. The ratio of the intensity at a point where the path difference is 3 to the maximum intensity in the pattern is

Step-by-step solution

Let the intensities of the two waves be I₁ = 4I₀ and I₂ = I₀ . The phase difference corresponding to a path difference of x = 3 is: = 2 x = 2 3 = 2 3 (or 120^ ) The intensity at this point is given by the interference formula: I_ point = I₁ + I₂ + 2 I₁ I₂ I_ point = 4I₀ + I₀ + 2 (4I₀)(I₀) (120^ ) I_ point = 5I₀ + 2(2I₀) (- 1 2 ) = 5I₀ - 2I₀ = 3I₀ The maximum intensity in the interference pattern is: I_ = ( I₁ + I₂ )^2 = ( 4I₀ + I₀ )^2 = (2 I₀ + I₀ )^2 = 9I₀ The required ratio is: I_ point I_ = 3I₀ 9I₀ = 1 3 Answer: