. The optical indicatrix and the transmission of light in crystals. ay as before it follows that rrj isa tangent line of the ray-surface, and is thus the intersection of thetangent plane at r with the plane EXOr. Let Or, Oij, intersect the ellipse in the points IV, G, respectively : thenOil and OG are respectively conjugate to OE and <JG, being perpen-dicular to 11X and GH, and therefore parallel to the tangents at 11 and G :the area of a parallelogram of which the adjacent sides are conjugateradii vectorcs is constant; hence nX-OTl = , by construction, ,,„ 1 ,„ 1 hence Or: 0R =
. The optical indicatrix and the transmission of light in crystals. ay as before it follows that rrj isa tangent line of the ray-surface, and is thus the intersection of thetangent plane at r with the plane EXOr. Let Or, Oij, intersect the ellipse in the points IV, G, respectively : thenOil and OG are respectively conjugate to OE and <JG, being perpen-dicular to 11X and GH, and therefore parallel to the tangents at 11 and G :the area of a parallelogram of which the adjacent sides are conjugateradii vectorcs is constant; hence nX-OTl = , by construction, ,,„ 1 ,„ 1 hence Or: 0R = O,i: OG, 50 THE TRANSMISSION OF LIGHT IN CRYSTALS. and the line rc] is therefore parallel to the tangent of the ellipse at 7?,and consequently to the line OU which is conjugate to Uli. Hence the ray-front corresponding to the ray Or intersects the trans-Terse plane BNOr perpendicularly in a line parallel to 07?. The diametral line Of, perpendicular to (Jli and lying in the plane IlSOr,is therefore normal to the ray-front corresponding to the ray Or (Fig. 12).. Fig. 11. Anabjtical Proof. The following is interesting to the mathematical student, by reason ofthe eliminations:— From Article 7 we have X y z ~ 1 hence _r--l? . ^ r-—b- ~ ~ r^—c^ (1). V T—a-Remembering thata?,-^. + ^2 + :p^^ 1 (Art. 7), we have \-ipf-\.--J = .-/. (2^ Also « + ^^% + (:2c.; ^o(Art. 7). (3). It is thug required to determine the tangent plane at a point xyz of the ray-surface in terms of the co-ordinates .r//c, which are connected by the above equations and also by the relation aVHZy^ + rV^ ==1. (4). THE RAY-FRONT CORRESPOXDIXG TO A GIVEN RAY. 51 (5). Forming the differential of each of the ec^uations (1), we have (r--a^) + = +.vbA{r^-P}bij +2 r>/br = Abu + yhA(,.2_(.2J^s: + 2 rzbr = Abz + :5^ Multiply these equations by , b^y, c^z, respectively, and add: thequantity bA is thus eliminated, for its coefficient (:L--\-lri/i/ -\-c^zzvanishes by relation (3); we
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