A crystal lattice is considered to be made up of regular layers or planes of particles (atoms, ions or molecules). These planes of particles are at equal distances from each other. When a beam of monochromatic x-rays is allowed to fall on a crystal these x-rays are diffracted and a large number of images of different intensities are formed. If the diffracted waves are in the same phase they interfere constructively and reinforce each other. As a result a series of bright spots are produced on the photographic plate placed in their path. On the other hand if the diffracted waves are out of phase they interfere destructively and cancel each other. As a result a series of dark spots are produced. According to the principles of reflection the path difference between any two spots is equal to the integral multiple of wavelength .

             (Bragg equation)

Where n = 1, 2, 3, 4,... and is known as the order of reflection. If n = 1, the order of reflection is one. If n = 2, the order of reflection is two and so on. The Eq gives relationship between the inter-planner distance d and the angle θ at which the x-rays of wavelength are reflected.

Due to the periodic nature of the scattering medium a scattered particle (photon, neutron, electron) can obtain momentum nk, where k isthereciprocal lattice vector. Generally speaking, the probability of the process drops down with increasing  momentum transfer (reflection order n), so n=1 gives the major reflection peak. However, if sinθ is so small that it is comparable to the Bragg angular width, then higher reflection orders n  become of importance. For example, low Bragg angle diffraction of of MeV electrons in crystals must be considered as multi-wave diffraction with various  n. There are other situations where higher order reflections are of importance, particularly,  if the unit cell contains many atoms, it may happen that n=1 reflection is suppressed due to destructive interference of the waves from the atoms..

Bragg law

2 d sinθ = nλ means that d is for particular Miller indices (hkl) as d h,k,l:

2 d h,k,l sinθ = nλ

it could be written as: 2 (d h,k,l /n) sinθ = λ

which is equivalent to 2 d nh,nk,nl sinθ = λ and written as (in short):

2 d sinθ = λ

means order of reflection is included in d, which is for particular Bragg indices (nh,nk,nl) here.

More discussion on:

https://www.researchgate.net/post/Why_is_the_first_order_of_diffraction_more_important_than_others_n1

A crystal lattice is considered to be made up of regular layers or planes of particles (atoms, ions or molecules). These planes of particles are at equal distances from each other. When a beam of monochromatic x-rays is allowed to fall on a crystal these x-rays are diffracted and a large number of images of different intensities are formed. If the diffracted waves are in the same phase they interfere constructively and reinforce each other. As a result a series of bright spots are produced on the photographic plate placed in their path. On the other hand if the diffracted waves are out of phase they interfere destructively and cancel each other. As a result a series of dark spots are produced. According to the principles of reflection the path difference between any two spots is equal to the integral multiple of wavelength .

             (Bragg equation)

Where n = 1, 2, 3, 4,... and is known as the order of reflection. If n = 1, the order of reflection is one. If n = 2, the order of reflection is two and so on. The Eq gives relationship between the inter-planner distance d and the angle θ at which the x-rays of wavelength are reflected.