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Question:

A light source, which emits two wavelengths λ₁=400nm and λ₂=600nm, is used in a Young's double slit experiment. If recorded fringe widths for λ₁ and λ₂ are β₁ and β₂, and the number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then which of the following statements are correct?

m₁>m₂

The angular separation of fringes for λ₁ is greater than λ₂

β₂>β₁

From the central maximum, 3rd maximum of λ₂ overlaps with 5th minimum of λ₁

Solution:

β=Dλ/d
λ₂>λ₁ ⇒ β₂>β₁
Also m₁β₁=m₂β₂ ⇒ m₁>m₂
Also 3(D/d)(600nm)=(2×5+1/2)(D/2d)400nm
Angular width θ=λ/d