# Why is the order of reflection simplified to n = 1?

My professor told us that for the sake of simplicity, we will assume that the order of reflection for Braggs' Law is always equal to 1 but failed to explain why. Is it because d(h,k,l) for materials has been determined using an order of reflection 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 $$d_{hkl}$$