The first diffraction minima due to a single slit diffraction is at $\mathrm{\theta }={30}^{\circ }$ for a light of wavelength 5000 A the width of the slit is 

The distance of first diffraction minimum from the central principal maximum, $\mathrm{x}=\mathrm{\lambda D}/\mathrm{d}$
$$\begin{gathered} \sin \mathrm{\theta }=\frac{\mathrm{x}}{\mathrm{D}}=\frac{\mathrm{\Lambda }}{\mathrm{d}}\text{ or }\mathrm{d}=\frac{\mathrm{\lambda }}{\sin \mathrm{\theta }} \\ =\frac{5000\times {10}^{-8}}{\sin 30}=2\times 5\times {10}^{-5} \\ =1.0\times {10}^{-4}m \end{gathered}$$