Resolving Power of a Prism

The theoretical resolving power of a prism (or grating) is given by 

FIGURE 3-9. Rayleigh criterion for resolution of spectral lines. 

Substituting the expression for dOjdn [(3-9)] into (3-14) at minimum deviation gives 

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Resolution of a Prism. The resolving power of a prism is given by... 

The above formula also assumes use of an infinitely narrow entrance slit, as does the formula for theoretical resolving power of a prism. The relation between theoretical and attainable resolution can be illustrated from Michelson s measurement of the wavelength of the green mercury line at 5641 A. Operating in the sixth order on a 10-in. ruled surface Michelson... 

Plot X against n and hence obtain the resolving power of a fused quartz prism, wifh a base length of 3.40 cm, at 200 nm, 250 nm, 300 nm and 350 nm. What is the resolution, in nanometres, at these wavelengths How would the resolving power and resolution be affected, quantitatively, by using two such prisms in tandem ... 

Thus, dispersion of the grating increases as d decreases (i.e., as the grating contains more lines per cm). Also, dispersion is not a function of k, and the linear dispersion is therefore a constant, unlike in the case of a prism. The resolving power of a diffraction grating is proportional to the size of the grating and the order of the diffraction used. 

The resolving power of a grating has the same dimensions as for a prism and use i again made of the Rayleigh criterion for resolution. The numerical value of the resolving power is given by X/AX, where AX meets the Rayleigh definition. 

The theoretical resolving power of a grating monochromator is identical to that derived for a prism. Hence the smaller the intergroove distance, the greater the resolution. 

Let us consider the attainable spectral resolving power of a spectrometer. When passing the dispersing element (prism or grating), a parallel beam composed of two monochromatic waves with wavelengths X and X -f AA. is split into two partial beams with the angular deviations 9 and 6> + A6> from their initial direction (Fig. 4.8). The angular separation is... 

Names such as spectrometer, spectroscope, spectrograph or monochromator are used for basically the same types of instruments, which are, however, applied in different ways. The principle of a prism spectrograph is illustrated in Fig.6.17. The resolving power is determined by the dispersion, dn/dA, and the length of the prism base b... 

The besl isolation of radiant energy can he achieved with flame spectrometers that incorporate either a prism sir grating monochromator, those with prisms having variable gauged entrance and exii slits. Both these spectrometers provide a continuous selection of wavelengths with resolving power sufficient lo separate completely most of the easily excited emission lines, and afford freedom from scattered radiation sufficient lo minimize interferences. Fused silica or quartz optical components are necessary to permit measurements in Ihe ultraviolet portion of the spectrum below 350 nanometers Sec also Analysis (Chemical) Atomic Spectroscopy Photometers and Spectra Instruments. 

Prism monochromators made of quartz have the great disadvantage of not being very useful below about 2500 A. As one goes to shorter wavelengths the transparency decreases and with it the resolving power. Much quartz also fluoresces in its own right. 

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