In a Young’s double slit experiment, the intensities at two points, for path differences λ/4 and λ/3, are I₁ and I₂ respectively. If I₀ denotes the intensity produced by each one of the individual slits, then (I₁ + I₂)/I₀ = ______.
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

In a Young’s double slit experiment, the intensities at two points, for path differences λ/4 and λ/3, are I₁ and I₂ respectively. If I₀ denotes the intensity produced by each one of the individual slits, then (I₁ + I₂)/I₀ = ______.

Physics · Circular Motion

JEE Mains 30 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

For equal slit intensities, I = 4I₀cos²(Δϕ/2). For Δ = λ/4, Δϕ = π/2, so I₁ = 4I₀cos²(π/4)=2I₀. For Δ = λ/3, Δϕ = 2π/3, so I₂ = 4I₀cos²(π/3)=I₀. Therefore (I₁+I₂)/I₀ = 3.