Grooves of a grating

The spectral resolving power discussed for the different instruments in the previous sections can be expressed in a more general way, which applies to all devices with spectral dispersion based on interference effects. Let As be the maximum path difference between interfering waves in the instrument, e.g., between the rays from the first and the last groove of a grating (Fig. 4.62a) or between the direct beam and a beam reflected m times in a Fabry-Perot interferometer (Fig. 4.62b). Two wavelengths X and X2 = + AX can still be... 

Note that (11.5) is completely analogous to the interference of coherent waves, diffracted by the grooves of a grating (see Sect.4.1). Replacing the product at by the optical path difference 6 between waves from adjacent grooves of the grating yields (4.26). While (4.26) describes the interference of stationary coherent waves in spaeoy (11.5) represents the interference of phase-ooupled waves of different frequencies on a time axis ... 

In the case of a grating, a slightly different form of this eqn. 7.2 is used, the path difference between two lines or grooves of distance d being expressed as a function of the angles a and... 

The resolving power of a grating thus is better in higher orders and for small groove spac-ings. It is also linear in the total number of grooves illuminated i.e., it is proportional to the width of the grating. 

Fig. 5 shows a parallel light beam incident onto two adjacent grooves of a diffraction grating. At a wavelength and an angle of incidence A normal to the grating surface, constructive interference for an angle B is obtained ... 

Dispersion of light at the surface of a grating occurs by diffraction. Diffraction of light occurs because of constructive interference between reflected light waves. The path of one wave is shown in Fig. 2.20. Parallel waves can be envisioned on adjacent grooves. Constructive interference or diffraction of light occurs when... 

The reciprocal linear dispersion for a grating is nearly constant over the entire wavelength region and it is dependent on the number of grooves per unit width, spectral order, and the focal length of the collimator. The resolution of a grating is a function of spectral order (m) and the total number of grooves N) ... 

The effective aperture width of a grating is the width of an individual groove (d) multiplied by the total number of grooves (N) and by cos r (r is the angle of reflection) ... 

With the grating equation disina — sin 0) = 1 of a grating with groove separation d and its dispersion dp/dX = / dcosP) for a given angle of incidence a (Vol. 1, Sect. 4.1.3), we obtain the spatial dispersion... 

Calculate the separation D of a grating pair that just compensates a spatial dispersion dS/dX = 10 for a center wavelength of 600 nm, a groove spacing of d= m. and angle of incidence a = 30°. 

Write the expression for resolution of a grating ruled to be most efficient in second order. To resolve a given pair of wavelengths, will you need more or fewer grooves if the grating were ruled in first order ... 

In a grating spectrometer, the interfering partial waves emitted from the different grooves of the grating all have the same amplitude. In contrast, in multiple-beam interferometers these partial waves are produced by multiple reflection at plane or curved surfaces and their amplitude decreases with increasing number of reflections. The resultant total intensity therefore differs from (4.25). 

A comparison with the resolving power v/Av = mN = NAs/X of a grating spectrometer with N grooves shows that the finesse F can indeed be regarded as the effective number of interfering partial waves and F As can be regarded as the maximum path difference between these waves. 

The dispersion of a grating refers to how broadly the monochromator disperses (or spreads) the light spectrum at the sample specimen position. Dispersion is generally expressed in units of nm per millimeter. Dispersion depends on the groove density (number of grooves per millimeter) of the grating. 

U Use Equation 7-13 for the resolving power of a grating monochromator to estimate the theoretical minimum size of a diffraction grating that would provide a profile of an atomic absorption line at 500 nm having a line width of 0.002 nm. Assume that the grating is to be used in the first order and that it has been ruled at 2400 grooves/mm. 

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