4. A diffraction pattern of a cubic crystal of lattice parameter (a 3.16 Å) is obtained with a monochromatic X-ray beam of wavelength 1.54 Å. The first line on this pattern was observed to have (O = 20.3°). Obtain the interplanar spacing and Miller indices of the reflecting plane? %3D

4. Two coherent beams having parallel electric fields are described by TT E₁ = 5 cos(ks₁ · wt + 3) E₂ = 3 cos +7) (ks₂ - wt+ With amplitudes in kV/m. the beams interfere at a point P where the phase difference due to path is π/4. At the point of superposition, calculate the net irradiance.

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

The hydrogen spectrum has a red line at 656 nm and a violet line at 434 nm. What angular separation between these two spectral lines is obtained with a diffraction grating that has 4172 lines/cm? (Assume that the light is incident normally on the grating.) first order separation     ° second order separation     ° third order separation     °