Index of refraction at various wavelengths for specified materials. color and wavelength red orange yellow green blue violet (660 (610 (580 (550 (470 (410 medium nm) nm) nm) nm) nm) nm) water 1.331 1.332 1.333 1.335 1.338 1.342 diamond 2.410 2.415 2.417 2.426 2.444 2.458 glass 1.512 1.514 1.518 1.519 1.524 1.530 (crown) glass (flint) 1.662 1.665 1.667 1.674 1.684 1.698 polystyrene 1.488 1.490 1.492 1.493 1.499 1.506 quart 1.455 1.456 1.458 1.459 1.462 1.468 (fused)

As a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let = 0.626 and d0 = 4.00 . Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure. Figure P3.38 Atomic planes in a cubic lattice.

The first-order Bragg angle for a certain crystal is 12.1°. What is the second-order angle?

X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a Bragg angle of 25.5°. What is the spacing between the scattering planes in this crystal?