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

Question

In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle 30° when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of : (A) sin- 1 ((1/4)) (B) sin- 1 ((2/3)) (C) sin- 1 ((1/2)) (D) sin- 1 ((3/4))

Tardigrade Admin · Accepted Answer

For first minima, sin30° =(λ /a)=(1/2) First secondary maxima will be at sinθ =(3 λ /2 a)=(3/2)((1/2))⇒ θ =sin- 1((3/4))

Q. In a diffraction pattern due to a single slit of width $^{'} a^{'},$ the first minimum is observed at an angle $3 0^{\circ}$ when light of wavelength $5000 Å$ is incident on the slit. The first secondary maximum is observed at an angle of :

$s i n^{- 1} (\frac{1}{4})$

$s i n^{- 1} (\frac{2}{3})$

$s i n^{- 1} (\frac{1}{2})$

$s i n^{- 1} (\frac{3}{4})$

For first minima, $s in 3 0^{\circ} = \frac{λ}{a} = \frac{1}{2}$
First secondary maxima will be at
$s in θ = \frac{3 λ}{2 a} = \frac{3}{2} (\frac{1}{2}) \Rightarrow θ = s i n^{- 1} (\frac{3}{4})$

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

sin−1(41​)

sin−1(32​)

sin−1(21​)

sin−1(43​)