Visible light of wavelength 6000 × 10–8 cm falls normally on single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60° from the central maximum. If the first minimum is produced at θ1, then θ1 is close to :

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Question

Visible light of wavelength 6000 × 10^–8 cm falls normally on single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60° from the central maximum. If the first minimum is produced at θ₁, then θ₁ is close to :

30º

10º

25º

45º

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For 2^nd minima

d sinθ = 2λ

$sinθ = \frac{\sqrt{3}}{2} (given)$

$\Rightarrow \frac{λ}{d} = \frac{\sqrt{3}}{4}$ ….(i)

So for 1^st minima is

$sinθ = \frac{λ}{d} = \frac{\sqrt{3}}{4}$ from equation (i)

θ = 25.65° (from sin table)

θ ≈ 25º