Bragg's equation is derived on the basis of constructive interference of X-rays. But, measuring the angle of incidence of X rays that gives most intense diffracted x-rays is done by hit and trial method and it is difficult. Instead, if distructive interference is considered, the angle of incidence that gives zero(least) intense x rays can be easily measured. Why it is not adopted?

DEAR SRINIVAS,

Bragg’s spectrometer is used to determine the wavelength of X-rays. Bragg’s spectrometer is similar in construction to an ordinary optical spectrometer.

X-rays from X-ray tubes are made to pass through two fine slits S₁ and S_2, which collimate it into a fine pencil. This fine X-ray beam is then made to fall upon the crystal ‘C’ (usually sodium chloride crystal) mounted on the spectrometer table. This table is capable of rotation about a vertical axis and its rotation can be read on a circular graduated scale S.

The reflected beam after passing through the slits S₃ and s₄ enters the ionisation  chamber. The X-rays entering the ionisation chamber ionize the gas, which causes a current to flow between the electrodes and the current can be measured by galvanometer G. The ionisation  current is a measure of the intensity of X-rays reflected by the crystal.

The ionisation  current is measured for different values of glancing angle. A graph is drawn between the glancing angle and ionisation  current. For certain values of glancing angle, the ionisation  current increases abruptly.
 

The first peak corresponds to first order, the second peak to second order and so on. From the graph, the glancing angles for different orders of reflection can be measured. Knowing the angle and the spacing d for the crystal, wavelength of X-rays can be determined. 

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