The Messenger of Mathematics Volume 23
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The Messenger of Mathematics Volume 23

The Messenger of Mathematics Volume 23


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About the Book

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1894 edition. Excerpt: ...Fellow of Gonville and Caius College, Cambridge. THE chief object of the following communication is to explain an elementary method of establishing the fundamental properties of the cardinal points of any optical instrument symmetrical about an axis. The method is also applied to determine the foci and focal lengths of a system of refractors, whose focal lengths and principal foci are given. The distinguishing feature of the investigation is that the relative positions of the refracting surfaces are defined by means of the distances between their principal foci instead of the distances between the surfaces themselves; some considerable simplification in the formulas is thereby efiected. To illustrate the method, the necessary formulas for finding the cardinal points of an eye are set out at full length. It is proposed, therefore, to establish the following known properties of an optical instrument. lf F and F' be the first and second principal foci, Q any point on the axis, Q' its image, m the magnification of a small object placed at Q, reckoned negative if the image is inverted, where f and f ' are the first and second focal lengths, and are such that where, u and p.' are the absolute refractive indices of the initial and final media. It is understood that lines measured from the first principal focus are to be regarded as positive, if measured opposite to the direction in which light passes through the instrument; and that lines from the second VOL. XXIII. G principal focus are positive, if measured in the opposite direction. These properties are easily established for a single refracting surface. To establish them for any system of refracting surfaces it will therefore be suflicicnt to show that, if they hold for each..


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Product Details
  • ISBN-13: 9781154926705
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1154926702
  • Publisher Date: 20 May 2014
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 73 gr


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