The Laue equations are equal to the Bragg equation if we denote the angle between the wave vectors * s* and

**s**_{0 }by 2θ (see diagram below), which makes the vector

*–*

**s**

**s**_{0 }normal to the lattice plane.

As the scattering of X-rays by an atom is assumed to be elastic (no loss in momentum), the magnitudes of the wave vectors are the same. Thus, * s* –

**s**_{0}becomes the base of an isosceles triangle with equal sides of I

**s**_{0}I and I

*I. We have:*

**s**Since (see previous article)

To find an expression for *d _{nh,nk,nl}* (see above diagram), we determine the scalar projection of

*(the vector linking two plane-intercept points on the*

**a**/h*a*-axis) on the vector

*–*

**s**

**s**_{0}to give:

Dividing both sides of eq20 by *h*, we have . So,

Substitute eq23 in eq24, we have the Bragg equation:

Since the Laue equations are equal to the Bragg equation if we denote the angle between the wave vectors * s* and

**s**_{0 }by 2θ, the Bragg equation is a specific form of the Laue equations with the condition of 2θ imposed.