Bragg's Law –

Consider a set of parallel lattice planer of crystal separated by distance d apart.

Suppose a narrow beam of X-rays of the wavelength $\lambda$ be incident upon these planes at angle $\theta$ as shown in figure.

The beam will be reflected in all the directions by atoms of  various atomic planes. Because the refractive index of the matter of crystal is very nearly equal to unity hence there is practically no bending of rays entering or leaving the crystal.

Consider a ray PA reflected at atom A in direction of AR from plane 1 and another ray QB reflected at another atom B in direction BS.

Now from A, draw 2 perpendiculars AC & AD an incident ray QB and reflected ray BS respectively. The path difference between these 2 rays is (CB+BD). The 2 reflected rays will be in phase or out of phase, it will depend upon this path difference. When the path difference is whole wavelength $\lambda$ or multiple of whole wavelength i.e. $n \lambda$, then the 2 rays will reinforce each other & produce an intense spot. Thus the conditions of reinforcement is $CB+BD=n \lambda$

$CB=BD=d\sin\theta$

$\therefore 2d\sin\theta=n\lambda$ where $n=1,2,3,.....integers$

 This relation is known as Bragg’s Law.

Powder Method –

In this, the incident monochromatic radiation strikes a finely powdered specimen or a fine grained polycrystalline specimen. Diffracted rays go out from individual crystals which are oriented with planes making an incident angle $\theta$ with the beam satisfying the Bragg’s equation $n\lambda=2d\sin\theta$.

Fig (a) shows the arrangement. The X-rays are made monochromatic by passing them through the filter F. A narrow beam of monochromatic X-rays limited by slits S1 & S2 falls on powdered specimen C. The film fits round the inner surface of the camera covering nearly the whole in circumference so that even the beams diffracting upto nearly 180° can be recorded. The strip of film is long horizontally so that only the arcs of circles appear on it on developing. The X-rays after falling on the powder pass out of camera through a hole cut in film to minimize the fogging due to direct something scattering. The traces on the film are as shown in fig (b). the crystal structure can be obtained from arrangement of traces.

Figure (a)

Figure (b)