# How to use *Resolving-power* in a sentence

The definition of a fine vertical line, and consequently the

**resolving power**for contiguous vertical lines, is thus independent of the vertical aperture of the instrument, a law of great importance in the theory of the spectroscope.The

**resolving power**of a telescope with circular or rectangular aperture is easily investigated experimentally.Merely to show the dependence of

**resolving power**on aperture it is not necessary to use a telescope at all.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.The statement of the law of

**resolving power**has been made in a form appropriate to the microscope, but it admits also of immediate application to the telescope.AdvertisementIf 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular

**resolving power**is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.The visibility of a star is a question of brightness simply, and has nothing to do with

**resolving power**.Throughout the operation of increasing the focal length, the

**resolving power**of the instrument, which depends only upon the aperture, remains unchanged; and we thus arrive at the rather startling conclusion that a telescope of any degree of**resolving power**might be constructed without an object-glass, if only there were no limit to the admissible focal length.As the minimum focal length increases with the square of the aperture, a quite impracticable distance would be required to rival the

**resolving power**of a modern telescope.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.AdvertisementWe will now consider the important subject of the

**resolving power**of gratings, as dependent upon the number of lines (n) and the order of the spectrum observed (m).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.It is especially to be noticed that the

**resolving power**does not depend directly upon the closeness of the ruling.If we now suppose half the grating cut away, so as to leave 1000 lines in half an inch, the dispersion will not be altered, while the brightness and

**resolving power**are halved.There is clearly no theoretical limit to the

**resolving power**of gratings, even in spectra of given order.AdvertisementIn 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.The optical effect as regards

**resolving power**is the same as with a grating of N lines in the nth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders.'We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the

**resolving power**.Lord Rayleigh's expression for the

**resolving power**of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image.Unfortunately considerations of luminosity compel the observer often to widen the slit much beyond the range within which the theoretical value of

**resolving power**holds in practice.AdvertisementWith an indefinitely narrow slit the purity is equal to the

**resolving power**.As purity and

**resolving power**are essentially positive quantities, n i in the above expression must be the greater of the two frequencies.With a slit equal in width to eight times the normal one the purity is reduced to o 45R, so that we lose rather more than half the

**resolving power**and increase the light 3.7 times.It follows that for observations in which light is a consideration spectroscopes should be used which give about twice the

**resolving power**of that actually required; we may then use a slit having a width of nearly eight times that of the normal one.Theoretical

**resolving power**can only be obtained when the whole collimator is filled with light and further (as pointed out by Lord Rayleigh in the course of discussion during a meeting of the " Optical Convention " in London, 1905) each portion of the collimator must be illuminated by each portion of the luminous source.AdvertisementEvery observer should not only record the

**resolving power**of the instrument he uses, but also the purity-factor as defined above.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.In the case of prisms the

**resolving power**ist (dµ/dX), where t is the effective thickness of the medium traversed by the ray.In interpreting the phenomena observed in a spectroscope, it is necessary to remember that the instrument, as pointed out by Lord Rayleigh, is itself a producer of homogeneity within the limits defined by its

**resolving power**.The lower limit of the

**resolving power**of the eye is reached when the distance is approximately 3438 times the size of the object.AdvertisementThis expresses I as the

**resolving power**in the case of direct lighting.The Fraunhofer formula permits the determination of the most useful magnification of such an objective in order to utilize its full

**resolving power**.The table shows at the same time the great superiority of the immersion-system over the dry-system with reference to the

**resolving power**.As the microscopist usually estimates the

**resolving power**according to the aperture with ordinary day-light, Kohler introduced the " relative**resolving power**" for ultra-violet light.Then the denominator of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real

**resolving power**.AdvertisementIf the magnification be greater than the

**resolving power**demands, the observation is not only needlessly made more difficult, but the entrance pupil is diminished, and with it a very considerable decrease of clearness, for with an objective of a certain aperture the size of the exit pupil depends upon the magnification.From the section Regulation of the Rays (above) it is seen that the

**resolving power**is opposed to the depth of definition, which is measured by the reciprocal of the numerical aperture, I/A.By dark-field illumination it is even possible to make such small details of objects perceptible as are below the limits of the

**resolving power**.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.The

**resolving power**of an objective depends on its numerical aperture.AdvertisementIf the numerical aperture be known the

**resolving power**is easily found.The

**resolving power**can also be determined by using different fine test objects.Our investigations and estimates of

**resolving power**have thus far proceeded upon the supposition that there are no optical imperfections, whether of the nature of,, a regular aberration or dependent upon irregularities of material and workmanship. In practice there will always be a certain aberration or error of phase, which we may also regard as the deviation of the actual wavesurface from its intended position.The

**resolving power**and the width of the emergent beam fix the optical character of the instrument.The sensitive vane or strip may then be placed behind the slit; its width will not affect the

**resolving power**though there may be a diminution of sensitiveness.AdvertisementThe contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the

**resolving power**of optical instruments.The actual finiteness of A imposes a limit upon the separating or

**resolving power**of an optical instrument.The reason of the augmentation of

**resolving power**with aperture will now be evident.