equations (4) and (5) above can be derived from bragg's equation with a little bit of trigonometry. try it for the simple cubic lattice: draw a cube, put x, y, z axes on it. then, draw two parallel planes one intersecting the three axes at distances a from the origin and the other one parallel to it either through the origin or through the cube corner opposite to the origin. figure 3(b) shows the same planes for an fcc structure. calculate the distance between the two planes as