Conception of a Catena of Vistas—Image formation in a catena of surface vistas—Law governing the inversion of the image in a catena of surface vistas—Methods of measuring the scale of the image obtained on the terminal plane of a catena of vistas—Determination of the scale of the terminal image of a catena, of vistas by dividing the numerical aperture of the opening angle (N.A.) by the numerical aperture of the closing angle (n.a.)—On the imaging of the successive optical planes of the original vista—Imaging of the apertural plane of an antecedent vista in the apertural planes of all the following vistas—Preliminary indications of the practical applications of the fact that the field upon which is imaged the apertural plane of the antecedent vista corresponds in area and position with the apertural plane of the following vista—Exploitation of the circumstance that the sectional measurement of the image of the aperture of the antecedent vista furnishes the sectional measurement of the Ramsden disc of the following vista—Exploitation of the circumstance that in a catena the apertural plane of every antecedent vista is imaged and available for scrutiny in the Ramsden disc of the terminal vista—Association of progressive restriction of the aperture with cumulative magnification, and preliminary indications of the significance of this progressive restriction of the aperture in connexion with the development of a critical image, and the limit of microscopic resolution.
1. Introductory.
We may most conveniently pass from the study of image formation by the vacant aperture, to the study of image formation by means of the lens-armed aperture, by comparing the course and configuration of a beam of light transmitted in a symmetrical manner through a lens-armed aperture with the course and configuration of a beam transmitted through the same vacant aperture.
The course of the beam, meaning thereby in each case the course followed by the axial ray which traverses the centre of the aperture, will in the two cases be essentially the same.
The configuration of the beam will, on the contrary, be very different. In the case of the vacant aperture the beam will, as is shown in Fig. 14, A, be represented upon the screen by aluminous disc which will expand as the distance between the receiving in screen and the aperture increases.
In the case of the lens-armed aperture, the beam may be laid down upon the screen according to circumstances, in the different forms indicated in Fig. 14, B, C, and D, and again with more detail in Figs. 15, 16 and 17.
In Fig. 14, B, and Fig. 15, we have a beam originating at a point lying between the principal focus upon the surface of the lens. The diagram shows that the delimiting rays—and what holds true of these holds true of all the included rays—are bent in by the lens in such a manner as to diminish the angle of divergence of the beam.
