A slit of width e 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 $\frac{\pi}{3}$?

$\sqrt{3}λ$

$\text{For single slit diffraction, maxima condition (approx): } e\sin\theta = \frac{(2m+1)\lambda}{2}$

$\text{First maximum: } m=1$

$e\sin\theta = \frac{3\lambda}{2}$

$\theta=\frac{\pi}{3} \Rightarrow \sin\theta=\frac{\sqrt{3}}{2}$

$e \cdot \frac{\sqrt{3}}{2} = \frac{3\lambda}{2}$

$e = \frac{3\lambda}{\sqrt{3}} = \sqrt{3}\lambda$

$e = \sqrt{3}\lambda$