A Chapter On Fresnels Theory of Double Refraction
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c 2 (cos & cos 6} Va 2 c 2 Again v v v 2 are the roots of the equation I 2 m 2 n 2 ^ Q Hence v 2 + v 2 = I 2 (b 2 + c 2 ) + m 2 (c 2 + a 2 ) + n 2 (a 2 + b 2 ) = a 2 + c 2 -(a 2 -c 2 )cos0cos<9'by (4) (6). v 2 v 2 = I 2 b 2 o 2 + m 2 c 2 a 2 + nV6 2, = aV - c 2 ^ 2 (a 2 - b 2 ) + nV (b 2 - c 2 ) ; 18 Theory of Double Refraction. .. 4v 1 V=4aV-(a 2 ~c 2 ){c 2 (cos^+cos^) 2 -a 2 (cos^-cos^) 2 }by(5), = 4aV+ (a 2 -c 2 ) 2 (cos 2 0+cos 2 0') -2 (a 4 -c 4 ) costfcos 0'. . . (7). Hence squaring (6) and subtracting (7) we get / T 2 - 2\2 ^_ / 2 2\2 f "| 2/3 2 ^' 2/1 2 ^O = (a 2 -c 2 ) 2 sin 2 0sin 2 0'; * 1 2 \ / * * \ /* From (6) and (8) we easily deduce by adding and subtracting /) 4- ff A j_ /?' "1 Vj 2 = a 2 sin 2 -= + c 2 cos 2 -= 2 0+(9' 2 + <9' I (9) ' V 2 2 = a 2 sm 2 - +c 2 cos 2 The results of equations (8) and (9) are easily seen to coin- cide with those deduced in a different manner in Salmon's Solid Geometry, Art. 245. Analogous results can be obtained for ray velocities from the reciprocal ellipsoid.
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You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read online
To quickly assess the difficulty of the text, read a short excerpt:
c 2 (cos & cos 6} Va 2 c 2 Again v v v 2 are the roots of the equation I 2 m 2 n 2 ^ Q Hence v 2 + v 2 = I 2 (b 2 + c 2 ) + m 2 (c 2 + a 2 ) + n 2 (a 2 + b 2 ) = a 2 + c 2 -(a 2 -c 2 )cos0cos<9'by (4) (6). v 2 v 2 = I 2 b 2 o 2 + m 2 c 2 a 2 + nV6 2, = aV - c 2 ^ 2 (a 2 - b 2 ) + nV (b 2 - c 2 ) ; 18 Theory of Double Refraction. .. 4v 1 V=4aV-(a 2 ~c 2 ){c 2 (cos^+cos^) 2 -a 2 (cos^-cos^) 2 }by(5), = 4aV+ (a 2 -c 2 ) 2 (cos 2 0+cos 2 0') -2 (a 4 -c 4 ) costfcos 0'. . . (7). Hence squaring (6) and subtracting (7) we get / T 2 - 2\2 ^_ / 2 2\2 f "| 2/3 2 ^' 2/1 2 ^O = (a 2 -c 2 ) 2 sin 2 0sin 2 0'; * 1 2 \ / * * \ /* From (6) and (8) we easily deduce by adding and subtracting /) 4- ff A j_ /?' "1 Vj 2 = a 2 sin 2 -= + c 2 cos 2 -= 2 0+(9' 2 + <9' I (9) ' V 2 2 = a 2 sm 2 - +c 2 cos 2 The results of equations (8) and (9) are easily seen to coin- cide with those deduced in a different manner in Salmon's Solid Geometry, Art. 245. Analogous results can be obtained for ray velocities from the reciprocal ellipsoid.
What to read after A Chapter On Fresnels Theory of Double Refraction?
You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read online
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