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
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- 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) mmThe 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 °
- 2- A dielectric mirror stack has four dielectric layers with alternating refractive indices n₁=1.4 and n2=1.5. Design the mirror such that it can operate at a free-space wavelength of 552nm.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 4014 lines/cm? (Assume that the light is incident normally on the grating.) first order separation ° second order separation ° third order separation °4
- the normal human eye can detect colors whose wavelengths range from 380 nm to about NOTE: 1 n m = 10 − 9 m ( o r 1 m = 10 9 n m ) Group of answer choices 600 nm. 750 nm. 550 nm. 650 nm.X-rays of wavelength equal to 0.134 nm give a first order diffraction from the surface of a crystal when the value of 0(theta) is 10.5°. Calculate the distance between the planes in the crystal parallel to the surface examined. Solve correctly please full explanation neededQ4:The change of refractive index transparent materials such as glass can be given by relationship with wavelength in (Cauchy equation) n = A + B. As the (A,B) are constants and wavelength in a vacuum o. Find the group velocity at ho %3D 500 nm and for a specific type of glass it has (A=1.5, B = 3x 104 (nm)²).
- 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.2- If you know that the Bragg's angle for the (111) plane is 0=25°, calculate the lattice constant (a), given that the wavelength of the x-rays used is 1.54Aº?6. The distance between two atomic planes for a material is 200 nm .find the x-ray wavelength that matches the smallest angle of Bragg scattering of 3° *