In estimating theoretically the resolving power on a double star we have to consider the illumination of the field due to the superposition of the two independent images.
According to our former standard, this gives the smallest difference of wave-lengths in a double line which can be just resolved; and we conclude that the resolving power of a grating depends only upon the total number of lines, and upon the order of the spectrum, without regard to any other considerations.
The actual finiteness of A imposes a limit upon the separating or resolving power of an optical instrument.
The resolving power and the width of the emergent beam fix the optical character of the instrument.
Merely to show the dependence of resolving power on aperture it is not necessary to use a telescope at all.
In the above discussion it has been supposed that the ruling is accurate, and we have seen that by increase of m a high resolving power is attainable with a moderate number of lines.
In other words, a sufficiently good and distinct image as the resolving power permits cannot be arrived at, until the elimination, or a sufficient diminution, of the spherical and chromatic aberrations has been brought about.
A rotation of this amount should therefore be easily visible, but the limits of resolving power are being approached; and the conclusion is independent of the focal length of the mirror, and of the employment of a telescope, provided of course that the reflected image is seen in focus, and that the full width of the mirror is utilized.
For the purpose of obtaining smaller deviation, one part of the compound acts in opposition to the other, the resolving power of the opposing portion must be deducted in calculating the power of the whole.
The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and n the total number of lines ruled on the grating.