Question

In Young's double-slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 14∘ rad by using the 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 1 and 2 are in the visible range (380nm to 740nm), their values are

• A. (A) 400nm,500nm
• B. (B) 2500nm,1250nm
• C. (C) 380nm,525nm
• D. (D) 380nm,500nm

Answer 1

Answer: (B)

(B) 2500nm,1250nm

Answer 2

Explanation:
dsin⁡θ= integral mutiple of λdsin⁡θ=nλ ∵θ is very small∴sin⁡θ=θSo,d⋅θ=nλ0.1 mm×14=nλ10−4×0.25×10−1=nλ2500×109=nλλ=2500×10−9nFor n=1λ1=2500×10−91λ1=2500×10−9λ1=2500nmFor n=2λ2=2500×10−92λ2=1250×10−9=1250nmSo d1=2500nmλ2=1250nmHence, the correct option is (B).