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Diffraction/Bragg's law : how does $2\theta$ come about?

I'm trying to get my head around a problem (I should have checked whether I had the answer in class, the exams are coming up now and I don't know if I'll get a lecturer response over the holidays) I ...
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Problem similar to Davison & Germer eksperiment but with more angles and the mirror reflection

The problem statement: Narrow beam of electrons hits an aluminium plate under an angle $\alpha=30^\circ$ according to the flat surface. We know the distance between two crystal planes in ...