Bragg's Law refers to the simple equation:

$nλ = 2d sinθ$.....(1)

Derived (by the English physicists Sir W.H. Bragg) to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (θ, q). The variable   is the distance between atomic layers in a crystal, and the variable  is the wavelength of the incident X-ray beam n is an integer

Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.

Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle.

The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom  (in figure).

The second beam continues to the next layer where it is scattered by atom . The second beam must travel the extra distance  if the two beams are to continue traveling adjacent and parallel.

This extra distance must be an integral  multiple of the wavelength  for the phases of the two beams to be the same:

$nλ= AB+BC $.....(2)

Recognizing  as the hypotenuse of the right triangle, we can use trigonometry to relate  to the distance (AB+BC). The distance  is opposite q so,

$AB= d sinθ$.....(3)

Because AB = BC equation (2) becomes,

$nλ=2AB$.....(4)

Substituting equation (3) in equation (4) we have,

$nλ=2 d sin⁡θ$

Hence, Bragg's Law has been derived.

To calculate d for (100)

$d_{hkl}=\dfrac{a}{\sqrt{h^2+k^2+l^2 }}$

$d_{hkl}=\dfrac{2.125}{\sqrt{1^2+0^2+0^2 }}$

$d_{hkl}=2.125A^\circ$

Using Bragg’s law for n=2;

$nλ=2d sin⁡θ$

$2\times 0.592\times 10^{-10}=2\times 2.125\times 10^{-10}\times sin⁡θ$

$sin⁡θ=0.278$

$\therefore θ=16.14$