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AP Physics 2
14.8 Double-Slit Interference and Diffraction Gratings
AdvancedMCQMathematicalProportional Analysis19.4k
A schematic diagram showing X-ray reflection from two parallel atomic planes. Two horizontal dashed lines represent parallel planes of atoms separated vertically by a distance labeled d. Two parallel incoming arrows representing Ray 1 and Ray 2 extend from the upper-left toward the planes, each forming a glancing angle labeled \theta with the horizontal planes. Ray 1 strikes the upper plane and reflects upward and to the right at angle \theta. Ray 2 passes the upper plane, strikes the lower plane directly below the reflection point of Ray 1, and reflects upward and to the right parallel to Ray 1 at angle \theta. A double-headed vertical arrow between the two horizontal dashed lines is labeled d. No other labels, lines, text, or axes appear.
X-ray reflection from adjacent lattice planes in a crystal.
Monochromatic X-rays of wavelength \(\lambda\) are incident at a glancing angle \(\theta\) on parallel atomic planes of a crystal separated by distance \(d\). First-order constructive interference is observed at this angle. The crystal is then replaced by a second crystal with lattice plane spacing \(d' = \dfrac{4}{3}d\), and X-rays of wavelength \(\lambda' = \dfrac{2}{3}\lambda\) are used. Which of the following expressions correctly relates the sine of the new glancing angle, \(\sin\theta'\), for the first-order maximum to \(\sin\theta\)?

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