Prism spectrometers

When passing a prism, a light ray is refracted by an angle e which depends on the prism angle e, the angle of incidence and the refractive index n of the prism material (see Fig.4.12). The minimum deviation e is obtained when the ray passes the prism parallel to the base g (symmetrical arrangement with = 2 = 0 ) this case one can derive the equation [4.5] 

This shows that the angular dispersion increases with the prism angle e hut 

Material Useful spectral range [ptn] 1 Refractive Dispersion index n d/dx [nm l]  

With a focal length f=100 cm for the camera lens one achieves a linear dispersion dx/dx = 0.12 mm/8 with the flint prism, but only 0.015 mm/% with the quartz prism. 

According to (4.21a), the theoretical maximum resolving power depends solely 

This shows that the angular dispersion increases with the prism angle 6, but does not depend on the size of the prism. 

The diameter a of the limiting aperture in a prism spectrometer is (Fig. 4.16) geos a 

According to (4.20a), the theoretical maximum resolving power depends solely on the base length g and on the spectral dispersion of the prism material. Because of the finite slit width b the resolution reached in practice is somewhat lower. The corresponding resolving power can be derived from (4.11) to be at most 

In Summary The advantage of a prism spectrometer is the unambiguous assignment of wavelengths, since the position S2(X) is a monotonic function of X. Its drawback is the moderate spectral resolution. It is mostly used for survey scans of extended spectral regions. 

Using the relation Pi - - P2 = for minimum refraction, where the light passes through the prism parallel to the baseline g of the prism we obtain 

0 = dai = —do 2. From Snellius law sina = n sinP we obtain the derivatives  

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Fig. 2.33. Self-constructed magnetic-prism spectrometer for a TEM/STEM (a) schematic diagram of set-up (b) photograph of the system with the prism opened.

A magnetic prism spectrometer is usually employed, in which a magnetic field is used to deflect all the electrons through about 90 degrees, as illustrated in Figure 5.39. 

For a prism spectrometer with a symmetrically arranged prism with the refractive index n at an angle 7 (Fig, 3.1-9), the angular dispersion is given by... 

Figure 3.1-9 The significant features of a prism spectrometer h length of the basis, 7 angle of the prism, D diameter of the collimator lens with the focal length /, 5 width and h length of the entrance slit.

Eqs. 3.1-19 and 3.1-25, which describe the relation between the characteristics of gratings and prisms and the theoretical resolving power Ro, give the optical conductance of grating and prism spectrometers. We may write... 

Gp, the optica] conductance per wavenumber of grating and prism spectrometers, is therefore described by ... 

In conclusion it can be stated that the spectral optical conductance for a prism spectrometer, a grating spectrometer, and a Michelson interferometer are approximately as 1 10 1000. 

Figure 3.4-3 a Infrared absorption spectrum of butadiene at a pressure of 107 mbar at room temperature, thickness 10 cm b infrared emission spectrum of the same sample at T = 800 K compared to the emission spectrum of a black body of 800 K, recorded with Lcitz prism spectrometer (Gutberlet, 1978). 

Equations (3.2) and (3.3) are approximate formulae for spectrometers of modem design without lenses. The actual value for the VG prism spectrometer used in our HB-501 STEM is about 1.8 pmeV. In parallel detection mode, the dispersion achieved is usually further magnified by quadmpole lenses. A single quadmpole produces a line focus. Two such lenses in series can act as a... 

Figure 2. Polarized IR spectra of sections of human dental enamel. Data collected with xlO magnification Schwarzschild-type reflecting microscope, NaCl prism spectrometer and selenium polarizer (Ford et al. 1958). [Figure 4.7 from Elliott (1994), reprinted with permission from Elsevier Science.]...

FIGURE 36.8 (a) Photograph of a spectrometer, (b) The prism spectrometer and (c) the absorption spectrometer. 

Two basic designs of prism spectrometer are commonly used for spectrochemical analytical purposes, the Cornu and the Littrow types. Many of these instruments are presently in use, although grating spectrometers are gradually replacing prism instruments. 

FIGURE 4-2. Schematic diagram of a Littrow prism spectrometer. 

A few of these instruments were imported and used in the USA. But flame photometry was uncommon there until the introduction of the Beckman total-consumption nebuHzer-burner, producing a turbulent oxyacetylene flame. It was used with a high-quality silica prism spectrometer, a photomultiplier detector, and very simple electronic nullbalancing circuitry. Flame emission analysis for many elements was thus widely practised until atomic absorption equipment became available. 

For prism spectrometers, the spectral transmission depends on the material of the prism and the lenses. Using fused quartz, the accessible spectral range spans from about 180 to 3000 nm. Below 180nm (vacuum-ultraviolet region), the whole spectrograph must be evacuated, and lithium fluoride or calcium fluoride must be used for the prism and the lenses, although most VUV spectrometers are equipped with reflection gratings and mirrors. 

Table 4.1. Refractive index and dispersion of some materials used in prism spectrometers...

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