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Question:

In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 140 rad by using light of wavelength λ₁. When the light of wavelength λ₂ is used, a bright fringe is seen at the same angle in the same setup. Given that λ₁ and λ₂ are in the visible range (380 nm to 740 nm), their values are?

380 nm,500 nm

625 nm,500 nm

400 nm,500 nm

380 nm,525 nm

Solution:

The correct option is B 625 nm, 500 nm
Path difference = dsinθ ≈ dθ = 0.1 × 140 mm = 2500 nm
For bright fringe, path difference must be an integral multiple of λ.
∴ 2500 = nλ₁ = mλ₂
∴ λ₁ = 625, λ₂ = 500 (from m = 5) (for n = 4).