The Optical Indicatrix and the Transmission of Light in Crystals

The Optical Indicatrix and the Transmission of Light in Crystals

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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. 1892 edition. Excerpt: ... 0/" and OG' are respectively conjugate to OR and OG, being perpendicular to RN and GH, and therefore parallel to the tangents at R and G: the area of a parallelogram of which the adjacent sides are conjugate radii vectores is constant; hence nN-OU'GH-OG'. Also, by construction, RN=o?' GH=o, j' hence Or: OR' = Og: OG', E and the line rg is therefore parallel to the tangent of the ellipse at R', and consequently to the line OR which is conjugate to OR'. Hence the ray-front corresponding to tho ray Or intorsects the transverse plane RNOr perpendicularly in a line parallel to OR. The diametral line Of, perpendicular to OR and lying in the plane RSOr, is therefore normal to the ray-front corresponding to the ray Or (Fig. 12). Analytical Proof. The following is interesting to the mathematical student, by reason of the eliminations: --From Article 7 we have On expanding the denominator, it will be found that the terms involving A mutually destroy each other, owing to the identity When multiplied out, this term is likewise found to be zero. Hence the numerator of the above expression is also zero, and we have the relation ly'z'd?-c)+mzW(e-a+nx'y'ia-&2) = 0. (8). But this is the condition (Art. 6) that the line Of may lie in the plane RON: hence the front-normal Of lies in the plane RNOr and is perpendicular to OR. Corollary 1. The inclination of a ray Or to its front-normal Of is the same as the inclination of the normal RN to the radius vector RO at the corresponding point R of the indicatrix (Fig. 12). Corollary 2. If a ray coincides with the central normal to its rayfront, its direction is perpendicular to an axis of the indicatrix. Corollary 3. If the ray Or lies in one of the symmetral planos of the indicatrix, the intersection of the...show more

Product details

  • Paperback | 42 pages
  • 189 x 246 x 2mm | 95g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236495837
  • 9781236495839