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In a diffraction pattern due to a single slit of width a the first minimum is observed at an angle 30 o when light of wavelength 5000   Å is incident on the slit. The first secondary maximum is observed at an angle of:

Options

  1. Asin - 1 ⁡ 1 4
  2. Bsin - 1 ⁡ 2 3
  3. Csin - 1 ⁡ 1 2
  4. Dsin - 1 ⁡ 3 4

Correct answer

D. sin - 1 ⁡ 3 4

Step-by-step solution

a sin ⁡ 30 = λ a sin ⁡ θ = 3 λ 2 sin ⁡ θ sin ⁡ 30 = 3 2 sin ⁡ θ = 3 2 × 1 2 sin ⁡ θ = 3 4 θ = sin ⁡ 3 4

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