Practice question

**Intensity at point** in double-slit I = I_max cos²(φ/2), φ = (2π/λ)Δ, for Δ=λ/4 φ=π/2 I= I_max cos²(π/4)= I_max/2 =2I₀, for Δ=λ/3 φ=2π/3 I= I_max cos²(π/3)= I_max×0.25= I₀, for Δ=5λ/8 φ=5π/4? Actually φ=2π×5/8=5π/4, cos²(5π/8)=?, path difference for destructive φ=(2n+1)π, constructive 2nπ. Bright fringe position x_n = (n λ D/d) . For the third bright fringe, n = 3 . λ = 4.6 × 10⁻⁷ m , d = 2.0 × 10⁻⁴ m , D = 2.0 m . x₃ = (3 × 4.6 × 10⁻⁷ × 2.0/2.0 × 10⁻⁴) = 6.9 × 10⁻³ m = 6.9 mm . Using Δ = d sinθ, y =