Chapter 4, Problem 12E

Analyzing crystal diffraction is intimately tied to the various different geometries in which the atoms can be arranged in three dimensions and upon their differing effectiveness in reflecting waves. To grasp some of the considerations without too much trouble, consider the simple square arrangement of identical atoms shown in the figure. In diagram (a), waves are incident at angle $\theta$

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with the crystal face and are detected at the same angle with the atomic plane. In diagram (b), the crystal has been rotated 45° counterclockwise, and waves are now incident upon planes comprising different sets of atoms. If in the orientation of diagram (b), constructive interference is noted only at an angle $\theta =40°$,at what angle(s) will constructive interference be found in the orientation of diagram (a)? (Note: The spacing between atoms is the same in each diagram.)