Fig. 189.—The Stages of Resolution.
Finally in Fig. 189b we have again the same valve under the same magnifying power, but here obtained from an objective of numerical aperture 60% above that used for the main figure. The sharp striæ now show their true character. They had their origin in lines of very clearly distinguished dots, which are perfectly distinct, and are due to the resolving power at last being sufficient to show the detail which previously merely formed a sharp linear diffraction pattern entirely incapable of being resolved into anything else by the eye, however much it might be magnified.
Here one has, set out in unmistakable terms, the same kind of differences which appear in viewing celestial detail through telescopes of various aperture. What cannot be seen at all with a low aperture may be seen with higher ones under totally different aspects; while in each case the apparent sharpness and clarity of the image is somewhat extraordinary.
Further in Fig. 189b in using the resolving power of the objective of high numerical aperture, the image may be quite wrecked by a little carelessness in focussing, or by mismanagement of light, so that one would hardly know that the valve had markings other than those seen with the objectives of lower aperture, and under these circumstances added magnification would do more harm than good. In precisely the same way mismanagement of the illumination in Fig. 189a would cause the striæ to vanish and with Navicula Lyra, as with many other diatoms, the resolution into striæ is a thing which often depends entirely on careful lighting, and the detail flashes into distinctness or vanishes with a suddenness which is altogether surprising. For “lighting” read “atmosphere,” and you have just the sort of conditions that exist in telescope vision.
With respect to magnifying powers what has already been said is sufficient to indicate that on the whole the lowest power which discloses to the eye the detail within the reach of the resolving power of the objective is the most satisfactory.
Every increase above this magnifies all the optical faults of the telescope and the atmospheric difficulties as well, beside decreasing the diameter of the emergent pencil which enters the eye, and thereby causing serious loss of acuity. For the eye like any other optical instrument loses resolving power with decrease of effective aperture, and, besides, a very narrow beam entering it is subject to the interference of entoptic defects, such as floating motes and the like, to a serious extent.
Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol., 35, 335) the effect of reduction of ocular aperture upon acuity. The curve shows very plainly that for emergent pencils below a millimeter (1/25 inch) in diameter, visual acuity falls off almost in direct proportion to the decreasing aperture. Below this figure there can be only incidental gains, such as may be due to opening up double stars and simultaneously so diminishing the general illumination as to render the margins of the star discs a little less conspicuous.
An emergent pencil of this diameter is not quite sufficient for the average eye to utilize fully the available resolving power and some excess of magnification even though it actually diminishes visual acuity materially, may be of some service.