Crystal structure of glass by Bragg’s law: The general relationship between the wavelength of the incident x ray, angle of incidence and spacing between the crystal planes of atoms is known as Braggg’s law, expressed mathematically as
2d sin θ = nλ
Where n is an integer, λ is the wavelength of the incident x ray, d is the interplanar spacing of the crystal or distance between the layers of atoms and θ is the angle of incidence.
1. Consider that the x ray of wavelength λ is incident on a crystal at an angle θ . The incident rays AB and PQ after reflection from the crystal lattice planes Y and Z travel along BC and QR
2. Let the spacing between the crystal lattice planes of atoms be d
3. Draw perpendiculars BD and BE from point B on PQ and Qr respectively. BD and BE are the perpendiculars from point B on lines PQ and PR respectively.
4. Thus the path difference between the two waves ABC and PQR is DQ + QE. The path of the wave PQR is longer than the path of the wave ABC by DQ+QE.
In the DBQ, sin θ = DQ/BQ
Therefore DQ = BQ sin θ
In the EBQ, sin θ = QE/BQ
Therefore QE = BQ sin θ
Path difference between two rays = DQ+QE
= BQ sin θ + BQ sin θ = 2 BQ sin θ
= 2d Sin θ since BQ =d
If the path difference 2d Sin θ is equal to the integral multiple of wave length of x ray, i.e. nλ, then constructive interference will occur between the reflected rays and they will reinforce each other and consequently the intensity of reflected beam is maximum.
Thus, for constructive interference to occur:
2d sin θ = nλ
This is known as Bragg’s law.