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Efficiency

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 by

[E=Akl/50a]

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.