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Question:

Distance of 5th dark fringe from centers is 4 mm. If D = 2 m, λ = 600 nm, then distance between slits is

3.25 mm

10.35 mm

1.35 mm

2.00 mm

Solution:

Correct option is A. 1.35 mm
Distance of nth dark fringe from center = (2n-1)β/2
Distance of 5th dark fringe from center = 9β/2
and β = λD/d
So, 9 × λ × D / 2 × d = 4 × 10⁻³
=> d = 9 × 6 × 10⁻⁷ × 2 / 2 × 4 × 10⁻³ = 1.35 mm.