I find problems on Bragg diffraction frustrating. I can't tell how the angles are defined, nor the "planes" in the crystal--they look arbitrary. Why can't I just draw a slash through the crystal at any angle I want and get diffraction off the angles I hit with the slash? Is it just that the intensity drops as the spacing of atoms increases? And how can I get more than one "order" of diffraction from the same crystal and wavelength? Isn't the reflection angle completely determined by the "Bragg angle" that defines a slice of crystal? It seems as if given a crystal, one could say, "these are the only possible angles for diffraction. If you use the right wavelength, you can see it. Otherwise, no diffraction anywhere." To repeat, how are the angles defined? Wikipedia is no help, I already know all of what they say in the entries. I tutor physics, and teach single slit, double slit, diffraction gratings and so forth every year. But Bragg diffraction defeats me. Suggestions?