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Diffraction of Light

Problem 5.155

A beam of X-rays with wavelength λ=174\lambda=174 pm falls on the surface of a single crystal rotating about its axis which is paral-lel to its surface and perpendicular to the direction of the incident beam. In this case the directions to the maxima of second and third order from the system of planes parallel to the surface of the single crystal form an angle α=60∘\alpha=60^{\circ} between them. Find the corresponding interplanar distance.

Reveal Answer
5.155. d=λ2sin⁡(α/2)k12+k22−2k1k2cos⁡(α/2)=0.28pm,d=\frac{\lambda}{2 \sin (\alpha / 2)} \sqrt{k_{1}^{2}+k_{2}^{2}-2 k_{1} k_{2} \cos (\alpha / 2)}=0.28 \mathrm{pm}, where k1k_{1} and k2k_{2} are the orders of reflection.
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