A slit of width is illuminated by light of wavelength λ. What should be the value of e to obtain the first maximum at an angle of diffraction of $\frac{\pi}{3}$?

$\frac{2}{\sqrt{3}}λ$

The correct answer is Option (1) → $\frac{2}{\sqrt{3}}λ$

The condition for minima in single-slit,

$a\sin θ=\left(m+\frac{1}{2}\right)λ$

and, first maxima occurs at $m=0$

$⇒a\sin\left(\frac{π}{3}\right)=\frac{λ}{2}$

$⇒a×\frac{\sqrt{3}}{2}=\frac{λ}{2}$

$⇒a=\frac{λ}{\sqrt{3}}$