The microscope and its revelations / by the late William B. Carpenter.

  • William Benjamin Carpenter
Date:
1891
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Licence: Public Domain Mark

Credit: The microscope and its revelations / by the late William B. Carpenter. Source: Wellcome Collection.

Provider: This material has been provided by The University of Leeds Library. The original may be consulted at The University of Leeds Library.

    73/1184 (page 45)
    HOW ' ArERTURE ' IS OBTAINED lucid exposition of Abbe's elaborate monographs that the English student is immensely indebted.' The definition of ' aperture' in its legitimate sense of ' opening' is shown by Abbe to be obtained when we compare the diameter of the pencil emergent from the objective with the focal length of that objective. It will be desirable to explain somewhat more in detail how this conclusion is arrived at, as given in Professor Abbe's papers. Taking in the first case a single-leTiS microscope, the number of rays admitted within one meridional plane of the lens evidently in- creases as the diameter of the lens (all other circumstances remaining the same), for in the microscope we have at the back of the lens the same circumstances as are in front in the case of the telescope. The larger or smaller number of emergent rays will therefore be properly measured by the clear diameter ; and, as no rays can emerge that have not first been admitted., this must also give the measure of the admitted rays. Suppose now that the focal lengths of the lenses compared are not the same—what, then, is the proper measure of the rays ad- mitted 1 If the two lenses have equal openings but different focal lengths,, they transmit the same number of rays to equal areas of an image at a definite distance, because they would admit the same number if an object were substituted for the image—that is, if the lens were used as a telescope-objective. But as the focal lengths are different, the amplification of the images is diflFerent also, and equal areas of these images correspond to diflferent areas of the object from which the rays are collected. Therefore the higher-power lens, with the same opening as the lower power, will admit a greater number of rays in all from the same object, because it admits the same number as the latter from a smaller portion of the object. Thus, if the focal lengths of two lenses are as 2 : 1, and the first amplifies N diameters, the second will amplify 2 N with the same distance of the image, so that the rays which are collected to a given field of 1 mm. diameter of the image are admitted from a field of A, rnra. in the first case aiicl of ~ mm. in the second. Inasmuch as the ' opening' of the objective is estimated by the diameter (and not by the area), the higher-power lens admits tivice as many rays as the lower power, because it admits the same number from a field of half the diameter,' and in general the admission of rays with the same opening but difierent powers must be in the inverse ratio of the focal lengths. In the case of the single lens, therefore, its aperture must be determined by the ratio hetiveen the clear ojoening and the focal length, m order to define the same thing as is denoted in the telescope by the absolute opening oo, ■■ 1 ■ o E^stimation of Aperture in the Microscope' (Abbe), Joimi. B.M.S. sei. 11 vol. 1. 388; Notes on Aperture, Microscopical Vision, and the Value of wide- f] mT'°'- »^^-303; ' The Aperture of Microscope Objectives,'