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Bragg's law

W. L. Bragg considered the diffraction as the consequence of contemporaneous reflections of the X-ray beam by various lattice planes belonging to the same family (physically, from the atoms lying on these planes). Let θ be the angle between the primary beam and the family of lattice planes with indices h, k, l. The difference in ’path’ between the waves scattered in D and B is equal to AB + BC = 2dsinθ.

Consider the triangles ABD and CBD, and notice how DB=d:

AB DB sinθ = d sinθ

and 

BC = DB sinθ = d sinθ 

Therefore, the total path difference between the tow rays (AB+BC) is equal to:

2d sin θ

For successive rays to reinforce, this difference must be a whole number of wavelengths. In other words, maximum positive interference will occur when:

=2d sin θ

Since the X-rays penetrate deeply in the crystal a large number of lattice planes will reflect the primary beam: the reflected waves will interfere destructively if the Bragg equation is not verified. The angle for which the Bragg equation is verified is the Bragg angle: for n=1,2,... we obtain reflections (or diffraction effects) of first order, second order, ..., relative to the same family of lattice planes H.