Prove that it is not possible to determine both wavelength of incident radiation and spacing of reflecting planes in a crystal by measuring the Bragg angles for several orders.

For the X- ray is incident on the crystal surface, then the angle of the incident is equal to angle of scattering and constructive interference will occur.

The Bragg’s law is used to calculate the coherent and incoherent scattering of the crystal.

Let assume $\lambda$is the wavelength of incident radiation and $d$is the spacing between the reflecting.

According to the Bragg’s law write the equation as:

$2d\sin \theta =m\lambda$

Here, $m$is the order number and$\theta$ is the Bragg’s angle.

From the above, if there are two values $m$and$\theta$ , then we can’t calculate the value of $d$and$\lambda$ until we would have the second equation to solve for the two unknown.

Hence it is proved that it is not possible to determine the wavelength of the incident radiation and spacing of reflecting plane.