In a diffraction pattern due to single slit of width ' a ', the first minimum is observed at an angle 3 0 ∘ when light of wavelength 5000 A ˚ is incident on the slit. The first secondary max

Question

In a diffraction pattern due to single slit of width ' a ', the first minimum is observed at an angle 3 0 ∘ when light of wavelength 5000 A ˚ is incident on the slit. The first secondary maximum is observed at an angle [ sin 30 = 2 1 ​ ]

TestHub · Accepted Answer

The condition for the first minimum in a single slit diffraction pattern is given by $a sin θ = λ$ .

Given $θ = 3 0^{\circ}$ , we have $a sin 3 0^{\circ} = λ$ .

$a (\frac{1}{2}) = λ \Rightarrow a = 2 λ$ .

The condition for the first secondary maximum is $a sin θ^{'} = \frac{3 λ}{2}$ .

Substituting $a = 2 λ$ , we get $2 λ sin θ^{'} = \frac{3 λ}{2}$ .

$sin θ^{'} = \frac{3}{4}$

$θ^{'} = sin^{- 1} (\frac{3}{4})$

Answer: $sin^{- 1} (\frac{3}{4})$

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