In a Young's double-slit experiment setup (Case 1), two slits are illuminated by a single monochromatic source, acting as coherent sources. The maximum intensity observed on the screen is I_ max . In another setup (Case 2), the two slits are replaced by two independent, incoherent monochromatic sources, each providing the same individual intensity on the screen as the slits did in Case 1. The resulting uniform intens

Step-by-step solution

Let the individual intensity of each source be I₀ . For Case 1 (coherent sources), the resultant intensity is given by I = I₁ + I₂ + 2 I₁ I₂ . The maximum intensity occurs when the phase difference = 0 . I_ max = I₀ + I₀ + 2 I₀ I₀ (0) = 4I₀ . For Case 2 (incoherent sources), the phase difference varies randomly and rapidly with time. The average value of is zero. Thus, the resultant uniform intensity is the simple sum of the individual intensities. I_ uni = I₀ + I₀ = 2I₀ . The ratio is I_ max I_ uni = 4I₀ 2I₀ = 2 1