Theoretically, a 1200 g/mm grating with a width of 110 mm that is used in first order has a numerical resolving power R = 1200 × 110 = 132,000. The numerical resolving power “R” should not be confused with the resolution or bandpass of an instrument system. N = the total number of grooves on the grating W g= the illuminated width of the grating Λ = the central wavelength of the spectral line to be resolved Two peaks are considered resolved if the distance between them is such that the maximum of one falls on the first minimum of the other. Resolution is then the ability of the instrument to separate adjacent spectral lines. Where, dλ is the difference in wavelength between two spectral lines of equal intensity. Resolving “power” is a theoretical concept and is given by: 3 shows a “flat field” spectrograph as used with a linear diode array. In a spectrograph, the linear dispersion for any wavelength other than the wavelength which is normal to the spectral plane will be modified by the cosine of the angle of inclination or tilt angle (γ) at wavelength λ n. Linear dispersion, therefore, varies directly with cos β, and inversely with the exit path length, L B, diffraction order (k), and groove density, n. In a monochromator, L B is the arm length from the focusing mirror to the exit slit, or if the grating is concave, from the grating to the exit slit. Where L B is the effective exit focal length in mm and dx is the unit interval in mm along the focal field (see Fig. Linear dispersion perpendicular to the diffracted beam at a central wavelength, λ, is given by: Linear dispersion is associated with an instrument’s ability to resolve fine spectral detail. The second instrument demonstrates “low” dispersion compared to the “higher” dispersion of the first. It is easy to imagine that fine spectral detail would be more easily identified in the first instrument than the second. For example, consider two spectrometers: one instrument disperses a 0.1 nm spectral segment over 1 mm while the other takes a 10 nm spectral segment and spreads it over 1 mm. Linear dispersion defines the extent to which a spectral interval is spread out across the focal field of a spectrometer and is expressed in nm/mm, Å/mm, cm -1/mm, etc.
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