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References

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  1. Houstoun—Treatise on Light, p. 36.
  2. Cf. Heath, Houstoun, and Southall, or any treatment of geometrical optics.
  3. Consult, e. g., Drude—Theory of Optics, p. 23 (Art. 23).

Drude,

Consult, e. g., Drude—Theory of Optics, p. 23 (Art. 23).

Heath,

Cf. Heath, Houstoun, and Southall, or any treatment of geometrical optics.

Houstoun,

Cf. Heath, Houstoun, and Southall, or any treatment of geometrical optics.

Houstoun—Treatise on Light, p. 36.

Southall,

Cf. Heath, Houstoun, and Southall, or any treatment of geometrical optics.

Other (3)

Houstoun—Treatise on Light, p. 36.

Cf. Heath, Houstoun, and Southall, or any treatment of geometrical optics.

Consult, e. g., Drude—Theory of Optics, p. 23 (Art. 23).

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Equations (28)

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n 2 u 2 - n 1 u 1 = n 2 - n 1 r 1
n 3 u 3 - n 2 u 2 - d 1 = n 3 - n 2 r 2
n k + 1 u k + 1 - n k u k - d k - 1 = n k + 1 - n k r k
u k + 1 = a k u k - b k c k u k - e k
a 1 = n 2 b 1 = 0 c 1 = n 2 - n 1 r 1 = p 1 e 1 = - n 1 a 2 = n 3 b 2 = n 3 d 2 c 2 = n 3 - n 2 r 2 = p 2 e 2 = - ( n 2 - p 2 d 1 )
u 2 = a 1 u 1 - b 1 c 1 u 1 - e 1
u 3 = a 2 u 2 - b 2 c 2 u 2 - e 2
u 3 = A 2 u 1 - B 2 C 2 u 1 - E 2
A 2 = | a 1 c 1 b 2 a 2 |             B 2 = | b 1 e 1 b 2 a 2 |             C 2 = | a 1 c 1 e 2 c 2 |             E 2 = | b 1 e 1 e 2 c 2 |
( u - E C ) ( v - A C ) = u v = AE - BC C 2
y 2 y 1 = n 1 tan 1 n 2 tan 2
n 1 tan 1 = n m tan m
n 1 y 1 u 1 1 = - n m y m v 1 1
n 1 v 1 = - n m u 1
- u I 1 = f = n 1 n m ( BC - AE C 2 ) - v I = f = ± n m n 1 ( BC - AE C 2 )
L = E C - f
L = A C - f
u m + 1 = A m u - B m C m u m - E m
A m = | a m b m C m - 1 A m - 1 |             B m = | a m b m E m - 1 B m - 1 |             C m = | c m e m C m - 1 A m - 1 |             E m = | c m e m E m - 1 B m - 1 |
A 3 = | a 1 c 1 0 b 2 a 2 b 3 e 2 c 2 a 3 |             B 3 = | b 1 e 1 0 b 2 a 2 b 3 e 2 c 2 a 3 |             C 3 = | a 1 c 1 0 b 2 a 2 e 3 e 2 c 2 c 3 |             E 3 = | b 1 e 1 0 b 2 a 2 e 3 e 2 c 2 c 3 |
A 6 = | a 1 c 1 0 0 0 0 b 2 a 2 b 3 e 3 0 0 e 2 c 2 a 3 c 3 0 0 0 0 b 4 a 4 b 5 e 5 0 0 e 4 c 4 a 5 c 5 0 0 0 0 b 6 a 6 |             B 6 = | b 1 e 1 0 0 0 0 b 2 a 2 b 3 e 3 0 0 e 2 c 2 a 3 c 3 0 0 0 0 b 4 a 4 b 5 e 5 0 0 e 4 c 4 a 5 c 5 0 0 0 0 b 6 a 6 | C 6 = | a 1 c 1 0 0 0 0 b 2 a 2 b 3 e 3 0 0 e 2 c 2 a 3 c 3 0 0 0 0 b 4 a 4 b 5 e 5 0 0 e 4 c 4 a 5 c 5 0 0 0 0 e 6 c 6 |             E 6 = | b 1 e 1 0 0 0 0 b 2 a 2 b 3 e 3 0 0 e 2 c 2 a 3 c 3 0 0 0 0 b 4 a 4 b 5 e 5 0 0 e 4 c 4 a 5 c 5 0 0 0 0 e 6 c 6 |
u 2 = a 1 u 1 - b 1 c 1 u 1 - e 1
u 2 = ( a 1 b 1 c 1 e 1 ) u 1
u 3 = ( a 2 b 2 c 2 e 2 )             u 2 = ( a 2 b 2 c 2 e 2 ) ( a 1 b 1 c 1 e 1 ) u 1
u 3 = ( a 2 a 1 - b 2 c 1 a 2 b 1 - b 2 e 1 c 2 a 1 - e 2 c 1 c 2 b 1 - e 2 e 1 ) u 1
u 3 = ( a 2 a 1 - b 2 c 1 ) u 1 - ( a 2 b 1 - b 2 e 1 ) ( c 2 a 1 - e 2 c 1 ) u 1 - ( c 2 b 1 - e 2 e 1 )
u 4 = ( a 3 b 3 c 3 e 3 ) ( a 2 b 2 c 2 e 2 ) ( a 1 b 1 c 1 e 1 ) u 1 = ( a 3 b 3 c 3 e 3 ) ( a 2 a 1 - b 2 c 1 a 2 b 1 - b 2 e 1 c 2 a 1 - e 2 c 1 c 2 b 1 - e 2 e 1 ) u 1 = ( a 3 ( a 2 a 1 - b 2 c 1 ) - b 3 ( c 2 a 1 - e 2 c 1 ) a 3 ( a 2 b 1 - b 2 e 1 ) - b 3 ( c 2 b 1 - e 2 e 1 ) c 3 ( a 2 a 1 - b 2 c 1 ) - e 3 ( c 2 a 1 - e 2 c 1 ) c 3 ( a 2 b 1 - b 2 e 1 ) - e 3 ( c 2 b 1 - e 2 e 1 ) ) u 1
u m + 1 = ( a m b m c m e m ) ( a m - 1 b m - 1 c m - 1 e m - 1 ) - - - - - - ( a 1 b 1 c 1 e 1 ) u 1