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  4. At what angles for the first-order diffraction, spacing between two planes respectively is λ and (λ/2)?

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Q. At what angles for the first-order diffraction, spacing between two planes respectively is $\lambda$ and $\frac{\lambda}{2}$?

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Solution:

$2d \,sin \,\theta = n\lambda$. (Bragg’s equation)
For $n = 1$
$2d \,sin \,\theta = \lambda$.
(i) If $\theta = 30^{\circ}$
$\Rightarrow 2d \,sin \,30^{\circ} = \lambda$
$\therefore d = \lambda$
(ii) If $\theta = 90^{\circ} = 2d \,sin \,90^{\circ} = \lambda$
$\Rightarrow d=\lambda/2$