Wave optics (Diffraction gratings) PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings • A diffraction grating is an extension of Young’s double slit and as such is based on both diffraction and interference, • The same equations apply to both double-slit interference and to diffraction produced by a diffraction grating. Grating :600~3000 per mm or more PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings • A diffraction grating consists of a great many parallel grooves drawn on a sheet of glass or plastic. • The light passes through the open intervals between grooves. The grating equation PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings For single slit Intensity of diffraction PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint For multiple slit the amplitude of the light passing through Diffraction gratings: effects of single slit +multiple slits PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings grating equation • It refers to the principal maxima. • Between any two adjacent maxima, there will be N -1 of zero intensity • Between these minima there are secondary maxima, but their intensities are much less than those in the principal maxima. • Note the sin2 N shows that the intensity of the principal maxima is proportional to the square of the number of slits. If there are more slits, the principal maxima become higher and higher and narrower and the secondary maxima between them get smaller and are suppressed PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings • The principal use of diffraction gratings is in spectroscopy. • Light of different wavelengths is diffracted at different angles, θ, and for each order, m, the blues nearer to the optic axis and the reds farther away from it. • The zeroth order retains the composite color of the source and therefore is easy to identify. grating equation PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings • The number of orders is limited by the separation of the lines. • A coarse grating, with relatively few lines per unit width, will give many orders. • A finely ruled grating may give only one or two orders, but their spectra will spread out much wider. grating equation PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Example: When looking through a diffraction grating at a hydrogen discharge tube, which emits light of 656 nm wavelength, we see two red lines, to either side of the zeroth order. If at a distance of 90 cm from the grating, the two lines are separated by 62.5 cm, how many lines per millimeter does the grating have? PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Diffraction gratings -Resolvance • Resolvance of a grating: ability to separate closely adjacent spectrum lines • The term dθ/dλ is the angular dispersion of the grating; increases as the order, m, increases, but not the resolvance λ / ∆λ • Consider that the light contains two wavelengths, λ and (λ + ∆λ)., PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Resolvance of the grating • Note that the resolvance, λ / ∆λ, is proportional to the number of lines, N, in the grating, and to the order, m, • To obtain higher resolution, either use a grating with more lines or go to a higher order. PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Example: The sodium D doublet has wavelengths of 589 nm and 589.6 nm. If only a grating with 400 rulings is available, what is the lowest order possible in which the D lines are resolved? PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Types of Gratings • Transmission gratings and Reflection gratings: either type can be made with more than 1000 lines per millimeter A blazed (輝躍式) reflection grating. Angle shown is blaze angle. PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Types of Gratings • A grating with completely opaque bars and clear intervals is called an amplitude grating. • If the bars do not block the light but merely retard its phase, we have a phase grating. • If the light distribution across the bars and intervals is sinusoidal rather than “square-wave”, all the light is diffracted into the two first order spectra. • Modern gratings are blazed. Whereas conventional gratings direct most of the light into the zeroth order, the advantage of blazed gratings is that they direct much more light into some of the higher orders, making more efficient use of the light available. PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Three-dimensional gratings • The light into a linear spread of wavelengths; they are ‘onedirnensional” gratings. • A two-dimensional or cross-grating results if two gratings are laid on top of each other, their rulings oriented at right angles. A zone plate could also be considered a two-dimensional grating, of rotational symmetry • Three-dimensional gratings: Xray diffraction • After Rontgen’s discovery of X rays, it was not known whether X rays were particles or waves of exceedingly short length. PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint Three-dimensional gratings • A crystal is a three-dimensional lattice of atoms, or groups of atoms, that is built out of repeating fundamental units, called unit cells. • X-ray diffraction may be visualized as reflections. Some of the incident rays are reflected at the top layer, but other rays penetrate to the deeper layers. The interplanar spacing is d. Γ = AB + BC = λ or mλ (max) Bragg’s Law. The same relationship holds if the X rays are transmitted through the crystal, PDF 檔案使用 "pdfFactory Pro" 試用版本建立 www.ahasoft.com.tw/FinePrint
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