In a single-slit diffraction pattern, the position of first secondary maximum is at 30° , then what will be the angular position of second minima?

Question

In a single-slit diffraction pattern, the position of first secondary maximum is at 30° , then what will be the angular position of second minima? (A) ( sin)- 1 (2 / 3) (B) ( sin)- 1 (.1.)  (C) ( sin)- 1 (1 / 2) (D) None

Tardigrade Admin · Accepted Answer

For first secondary maxima, sin(θ )1=(1 + (1/2))(λ /a)=(3 λ /2 a) ⇒ sin30o=(3 λ /2 a) ⇒ (λ /a)=(1/3) For second minima, sin θ =(2 λ /a)=(2/3) or θ =( sin)- 1 (2 / 3)

Q. In a single-slit diffraction pattern, the position of first secondary maximum is at $3 0^{\circ}$ , then what will be the angular position of second minima?

$(sin)^{- 1} (2/3)$

$(sin)^{- 1} (1)$

$(sin)^{- 1} (1/2)$

None

For first secondary maxima,
$sin (θ)_{1} = (1 + \frac{1}{2}) \frac{λ}{a} = \frac{3 λ}{2 a}$ $\Rightarrow sin 3 0^{o} = \frac{3 λ}{2 a}$
$\Rightarrow \frac{λ}{a} = \frac{1}{3}$
For second minima,
$sin θ = \frac{2 λ}{a} = \frac{2}{3}$
or $θ = (sin)^{- 1} (2/3)$

Q. In a single-slit diffraction pattern, the position of first secondary maximum is at 30∘ , then what will be the angular position of second minima?

(sin)−1(2/3)

(sin)−1(1)

(sin)−1(1/2)