In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle (1/40) 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 set up. Given that λ1 and λ2 are in visible range (380 nm to 740 nm), their values are :

Question

In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle (1/40) 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 set up. Given that λ1 and λ2 are in visible range (380 nm to 740 nm), their values are : (A) 380 nm, 500 nm (B) 625 nm, 500 nm (C) 380 nm, 525 nm (D) 400 nm, 500 nm

Tardigrade Admin · Accepted Answer

Path difference = d sin θ ≈ dθ = 0.1 × (1/40) mm = 2500 nm or bright fringe, path difference must be integral multiple of λ ∴ 2500 = n λ1 = m λ2 ∴ λ1 = 625 , λ2 = 500 (from m = 5) (for n = 4)

380 nm, 500 nm

625 nm, 500 nm

380 nm, 525 nm

400 nm, 500 nm

Path difference = dsinθ≈dθ =0.1×401​mm=2500nm or bright fringe, path difference must be integral multiple of λ ∴2500=nλ1​=mλ2​ ∴λ1​=625,λ2​=500 (from m=5) (for n=4)

Path difference = $d sin θ \approx d θ$
$= 0.1 \times \frac{1}{40} mm = 2500 nm$
or bright fringe, path difference must be integral multiple of $λ$
$∴ 2500 = n λ_{1} = m λ_{2}$
$∴ λ_{1} = 625, λ_{2} = 500$ (from $m = 5$ )
(for $n = 4$ )