One of the qualities for which a dispersive apparatus is considered better than another is that of succeeding in separating monochromatic components whose wavelengths differ from each other less than another instrument succeeds in separating.
One of the parameters characterizing a dispersive apparatus is its resolving power, which is given by the ratio between the wavelength of a monochromatic component and the difference in wavelength between that and the closest monochromatic component that that apparatus succeeds in separating.
Since establishing when two lines can be considered distinct is an extremely subjective operation, it is necessary each time to resort to Lord Rayleigh's criterion, according to which two lines of equal intensity, corresponding to different wavelengths in the spectrum of a given order, can be considered distinct when the maximum of the one coincides with the minimum of the adjacent one at the maximum of the same order.
In the case of a flat grating, on using Lord Rayleigh's criterion and the conditions of maximum and minimum, it is found that the resolving power is given by the product of order m of the spectrum for the number N of segments actually struck by the beam of light to be analysed.
To increase the resolving power of flat gratings, not being able to go beyond the third or fourth order of the spectrum owing to superimposition and poor luminosity, it was attempted to increase the number of segments up to the centimetre, but with this approach progress was limited. Even attempts to construct gratings that would direct all, or almost all, the diffracted light to the spectrum of a given order was only partially successful and more or less casual. ...continues