In Young’s double-slit experiment, slits are 2 mm apart and illuminated by wavelengths λ₁ = 12000 Å and λ₂ = 10000 Å. At what minimum distance from central common bright fringe will a bright fringe of one pattern coincide with a bright fringe of the other?
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Question

In Young’s double-slit experiment, slits are 2 mm apart and illuminated by wavelengths λ₁ = 12000 Å and λ₂ = 10000 Å. At what minimum distance from central common bright fringe will a bright fringe of one pattern coincide with a bright fringe of the other?

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G1 Physics · Accepted Answer

Step 1: Coincident bright fringes satisfy n₁λ₁ = n₂λ₂. Step 2: n₁/n₂ = λ₂/λ₁ = 10000/12000 = 5/6, so smallest n₁ = 5 and n₂ = 6. Step 3: y = n₁λ₁D/d, using D = 2 m, d = 2 × 10⁻³ m, λ₁ = 1.2 × 10⁻⁶ m. Step 4: y = 5 × (1.2 × 10⁻⁶) × 2/(2 × 10⁻³) = 6 × 10⁻³ m. Final answer: (B) 6 mm.