The product of resolving power and luminosity is commonly known
as efficiency. In normal operation, reducing the width of
the entrance slit will increase the resolving power but reduce the
luminosity while the efficiency remains fixed. Efficiency is therefore
a useful means for comparing the performance of two spectrometers.
For a grating spectrometer, the efficiency, E, is given
where A is the area of the aperture stop of
the spectrometer (ideally, the grating), k the order of diffraction, a the grating constant (i.e. the width of a groove on the
grating). The length of the entrance slit is assumed to be 1/50th
of the focal length of the spectrometer.