The pupil of an optical system with regard to perspective

• Published in: Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character Containing papers of a mathematical and physical character, 1911-08, Vol.85 (580), p.462-470
• Main Author: Beck, Conrad
• Format: Article
• Language: English
• Subjects: Geometric planes; Optical focus; Optical lenses; Parallel lines; Photographic lenses; Photographic plates; Telephoto lenses
• ISSN: 0950-1207; 2053-9150
• DOI: 10.1098/rspa.1911.0058

Hitherto the use made of the so-called “entrance and exit pupil” of an optical system has been chiefly in regard to aperture and the questions which are related thereto. I have been led to investigate this conception more completely, and I have now found that it may be used with advantage as an additional factor, in connection with the Gauss planes, for explaining the action of optical instruments as regards the perspective of the images formed. The Gauss planes enable us to refer the action of a complicated optical system to an equivalent single lens placed in two positions—the entrance equivalent plane and the exit equivalent plane. In fig. 1, the upper half of the diagram shows the course of a ray of light from X passing through the three lenses to X', each lens bending the light to a certain extent. The lower half of the diagram shows a lens of the correct equivalent focus placed at E to receive the light, and at E' to discharge it. This will act in a similar manner to the complete system, and many of the properties of the optical system may be correctly studied by confining our attention to an equivalent single lens, placed in the plane E to receive the light, and shifted to the plane E' to discharge it. By this means, assuming that the optical system is corrected in such a manner that the oblique rays and those far from the axis act in the same manner as the direct axial rays, the position and size of images can be determined with accuracy; but the perspective of the image cannot be correctly explained by aid of the Gauss planes alone. The “pupils” used as a modifying factor in connection with the Gauss planes will explain this apparent discrepancy.