In a Fraunhofer diffraction at single slit of width $\mathrm{d}$ with incident light of wavelength $5500 \mathrm{\AA },$ the first minimum is observed, at angle $30°$. The first secondary maximum is observed at an angle $\mathrm{\theta }=$ 

Slit width $=\mathrm{d}$

$\mathrm{\lambda }= 5500 \mathrm{\AA }=5.5\times {10}^{-7} \mathrm{m}, {\mathrm{\theta }}_1=30°$

For first secondary minima, $\mathrm{d} {\mathrm{sin\theta }}_1=\mathrm{\lambda }$

$\mathrm{d}=\frac{\mathrm{\lambda }}{\sin {\mathrm{\theta }}_{\mathrm{n}}}=\frac{5.5\times {10}^{-7}}{\sin 30°}=11\times {10}^{-7} \mathrm{m}$

For first secondary maxima, $\mathrm{dsin\theta }=\frac{3\mathrm{\lambda }}{2}$

i.e. $\mathrm{sin\theta }=\frac{3\mathrm{\lambda }}{2\mathrm{d}}=\frac{3\times 5.5\times {10}^{-7}}{2\times 11\times {10}^{-7}}$

$$\begin{gathered} \mathrm{sin\theta }=\frac{3}{4} \\ \Rightarrow \mathrm{\theta }={\sin }^{-1}\left(\frac{3}{4}\right) \end{gathered}$$