Why is the order of reflection simplified to n = 1?
The common form of the Bragg equation is $\lambda=d_{hkl}\sin(\theta)$ but in crystallography it is used as $\displaystyle \lambda =\frac{2d_{hkl}}{n}\sin(\theta)=2d_{nh,nk,nl}\sin(\theta)$ where the indices are divided through by $n$ to give $\lambda=d_{hkl}\sin(\theta)$. The indices $hkl$ have to be integers (from derivation via Laue equations) but can also be multiples of integers, i.e. they can have a common factor. When the $hkl$ do have a common factor they are not strictly lattice planes but planes parallel to $(h/n, k/n,l/n)$ with a spacing $1/n$ of the lattice. Suppose a plane is (210) then each lattice plane passes through a lattice point (atom). If the indices were (420) then not all planes are equivalent as only half of the points (atoms) pass through a lattice plane so they are not equivalent. Thus sticking with $n=1$ ensures we always use for example, (210), and not (420) or (630) etc., and so always calculate the correct value for $d_{hkl}$