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 mathring A 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 mathring A is incident on the slit. The first secondary maximum is observed at an angle of : (A)  sin-1 ( (2/3) ) (B)  sin-1 ( (1/2) ) (C)  sin-1 ( (3/4) ) (D)  sin-1 ( (1/4) )

Tardigrade Admin · Accepted Answer

For first minima , sin 30° = (λ/a) = (1/2) First secondary maxima will be at sin θ = (3 λ/2a) = (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 $5000 \overset{˚}{A}$ is incident on the slit. The first secondary maximum is observed at an angle of :

$sin^{- 1} (\frac{2}{3})$

$sin^{- 1} (\frac{1}{2})$

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

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

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

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 5000A˚ is incident on the slit. The first secondary maximum is observed at an angle of :

sin−1(32​)

sin−1(21​)

sin−1(43​)

sin−1(41​)