Today I learned about Miller indices in a cubic crystal, and I learned that adjacent planes $(hkl)$ in a simple cubic crystal are spaced a distance $d_{hkl}$ from each other, with $d_{hkl}$ given by:
$$d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$$
For example, take the origin any of the below vertices of the cube with z axis directed upwards, the $(0 0 2)$ plane cuts horizontally the middle of the cube, and for this set of planes, $d_{hkl} = \frac{a}{2}$.
May be a silly question, but if we followed the rule of spacing, we would get that the next $(0 0 2)$ plane is the very upper horizontal plane in the cube, which - i guess - is not true since the latter plane has $(0 0 1)$ and not in any case $(0 0 2)$ miller indices. However, if we considered that $(0 0 2)$ planes are only those passing horizontally through the middle of unit cells, then the distance between them will equal $a$ and not $\frac{a}{2}$ (using imagination and not rules).
I must be missing something very trivial here, but it is only today that i started learning these stuff and i am really confused. Thanks for help.