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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 download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1894 Excerpt: ...induction, that the formula? (1), (2), (3) must hold for any system of refracting surfaces, since they are known to hold for a single refractor. The principal points H, H or points of unit magnification, are determined by the equations FH=-f, FH' =-f. It follows immediately, from Ilelmholtz's formula connecting the magnification at a point with the inclinations to the axis of a ray through the point before and after refraction (Heath's Optics, Art. 50), that the points N N't determined by the equations FN=-f, F'N' =-f, a 2. possess the property that any incident ray through N emerges through N' parallel to its original direction. These points N, N' are the nodal points. The preceding results may be used to obtain the foci and focal lengths of any system of refractors, whose foci and focal lengths are given. Let F, and Ft', Ft and F, ', ..., Fn and Fn' be the principal foci of the refractors; f and/, ', ..., / and/n' their focal lengths; and let FJFc #, f, '=c, ..., FnFpJ=cK_bn, so that c is positive if the direction from Ft to Fx is opposite to the direction of light. Let FJr, FJ, flr, /J be the foci and focal lengths of the combination of the refractors numbered 1,2, 3, ..., r. Using the principle of the reversibility of a ray of light, we can now write down the formula to find Fln, viz., Cl- CM C84 Cn-1, - The foci of the combination of n refractors are therefore determined. The focal lengths are determined by the following equations: --It 5;uows from tieae equations tiat-f, /, -/, H equal to tie numerat)r of tie last convergent to tie continued fraction, If therefore JT denotes this last numerator, f f' J---i--Li--...........-..-.'-J im Not it ias been proved tiat, if /t ami -. are tie indices of tie era and Last meuia, A, A


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Product Details
  • ISBN-13: 9781130346350
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130346358
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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