Practice question

**Incoherent sources** intensity adds I = I₁+I₂, no interference pattern because phase random, two independent sources cannot produce stable interference because phase difference fluctuates rapidly, coherent sources required with constant phase, laser coherent, visibility of fringes requires coherence, degree of coherence determines contrast. Dark fringe position x_n = ((n + (1/2)) λ D/d) . For the third dark fringe, n = 2 . λ = 6.0 × 10⁻⁷ m , d = 4.0 × 10⁻⁴ m , D = 2.0 m . x₂ = ((2 + (1/2)) × 6.0 × 10⁻⁷ × 2.0/4.0 × 10⁻⁴) = (2.5 × 1.2 × 10⁻⁶/4.0 × 10⁻⁴) = 7.5