There is a circular slit with its radius a = 0.1mm. The distance between the slit plane and detector plane is given by R=1m. Roughly estimate the requirement of the wavelength of incident light for Fraunhofer diffraction with appropriate justification.

Figure 3.22 shows an x-ray diffraction pattern for a-iron taken using a diffractometer and monochromatic x-radiation having a wave- length of 0.1542 nm; each diffraction peak on the pattern has been indexed. Compute the interplanar spacing for each set of planes in- dexed; also determine the lattice parameter of Fe for each of the peaks. Figure 3.22 Diffraction pattern for polycrystalline a-iron. (110) (211) (200) 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 Diffraction angle 20 Intensity (rel ative)

A parallel beam of monochromatic light of wavelength 500nm passes through a slit of width 0. 5mm. Find the angular divergence in which most of the light is diffracted.

X - rays of wavelength 0.140 nm are reflected from a certain crystal, and the first - order maximum occurs at an angle of 14.4°. What value does this give for the interplanar spacing of the crystal?

You measure the distance between the finges of a diffraction pattern as follows: Distance (mm): 3.01, 3.27, 3.28 You measure the distance eight additional times to obtain the following ten values: Distance (mm): 3.01, 3.27, 3.28, 3.31, 3.16, 3.17, 3.15, 3.25, 3.18, 1.46 What values for the distance and uncertainty would you report using the first three measurements and the entire set of ten measurements? Group of answer choices First three: (3.22 ± 0.03) mm, All ten: (3.22 ± 0.02) mm First three: (3.19 ± 0.09) mm, All ten: (3.0 ± 0.2) mm First three: (3.186667 ± 0.07216237) mm, All ten: (3.201000 ± 0.02613236) mm First three: (3.216667 ± 0.02880329) mm, All ten: (3.216000 ± 0.02379916) mm First three: (3.240000 ± 0.04082483) mm, All ten: (3.217000 ± 0.02702036) mm First three: (3.24 ± 0.04) mm, All ten: (3.22 ± 0.03) mm

Light from a slit passes through a transmission diffraction grating of 400 lines/mm, which is located 3.0 m from a screen. What are the distances on the screen (from the unscattered slit image) of the three brightest visible (fi rst-order) hydrogen lines?

The dispersion curve of glass is the curve that describes how the index of refraction of glass changes as a function of the wavelength. This curve can be represented approximately by Cauchy's empirical equation, n = A + B/2² where for a specific glass in question A = 1.40 and B = 2.5 × 10 nm² (yes, those units are nanometer squared). Find the phase and group velocities for light of 500nm wavelength in that glass.

PROBLEM For a given x-ray diffraction test (n = 1) on a cubic crystal structure, the recorded diffraction peaks (20) were 24.09°, 34.33°, 42.37°, 49.33°, 55.62°, and 61.48°. The x-ray wavelength used in the test was 0.15418 nm. For this test, determine the crystal structure of the element, the lattice constant, and identify the element.

Incident nA = SQ + QT (3.19) na = dnki sin 0+ dnki sin 0 (3.20) = 2drki sin 0 H.W. Derive equation 3.20 (Bragg's Law) from equation 3.19 using trigonometry formulas.

If the wavelength l of the X­rays is too large relative to the spacing of planes in the crystal, no Bragg diffraction will be seen because sin u would be larger than 1 in the Bragg equation, even for n 5 1. Calculate the longest wavelength of X­rays that can give Bragg diffraction from a set of planes separated by 4.20 Å.