At what angles for the first order diffraction, spacing between two planes respectively are $\lambda \text{ and }\frac{\lambda }{2}$?

$$\begin{gathered} 2\mathrm{d} \sin \mathrm{\theta } = \mathrm{n\lambda } (\mathrm{Bragg}\text{'}\mathrm{s} \mathrm{eqn}) \\ \mathrm{for} \mathrm{n} = 1, 2\mathrm{d} \sin \mathrm{\theta } = \mathrm{\lambda } \\ \left(\mathrm{i}\right) \mathrm{If} \mathrm{\theta } = 30°\Rightarrow 2\mathrm{d} \sin 30° = \mathrm{\lambda } \\ \therefore \mathrm{d} = \mathrm{\lambda } \\ \text{ (ii) If }\mathrm{\theta }={90}^{\circ }\Rightarrow 2\mathrm{dsin}{90}^{\circ }=\mathrm{\lambda } \\ \therefore \mathrm{d}=\mathrm{\lambda }/2 \end{gathered}$$