The Resolving Power Attainable in X-ray Spectroscopy by Photographic Methods

If $w_c$, the (half) range of glancing angle over which a crystal will reflect monochromatic x-rays, has been determined by the double spectrometer method, it is possible to calculate what resolving power is attainable from this crystal by photographic methods. Equations are set up giving the resolving power in terms of $a$, the slit width, and $R$, the distance from slit to photographic plate. Some results are: (1) No appreciable increase in resolving power is attainable by making $\frac{a}{2R}<\frac{1}{4}{w}_c$. (2) If $\frac{a}{2R}>3\mathrm{}{w}_c$, the resolving power does not involve $w_c$. (3) The resolving power attainable in the first order is ${1/2}^{1/2}$ of that attainable in a double spectrometer with crystals of equal perfection. Equations are also derived by which observed line widths in photographic spectrometers may be corrected for slit and crystal diffraction pattern effects. The results are applied to recent experimental results with photographic spectrometers and it is shown that the width of $\mathrm{Mo}K{\alpha }_1$ observed photographically is considerably greater than the values obtained by the double spectrometer.