Abstract

No abstract available.

Full Article  |  PDF Article

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Diagram of the investigated optical system.

Fig. 2a
Fig. 2a

A three-dimensional representation of the optical system, indicating the geometrical construction necessary for evaluation of the path length of the ray (h, r, α) through a solution of unit refractive index.

Fig. 2b
Fig. 2b

Diagram illustrating the relation between the path length of a ray through a solution of unit refractive index and that through a solution of refractive index n.

Tables (1)

Tables Icon

Table I Examples of the percentage errors introduced in T and μl by assuming ideal photometric conditions. The calculations were made with the aid of Eqs. (6a), (7a), (8) and (9), for a μl value of 4.6 (i.e. T→0.01).

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

t = l [ 1 + h 2 p 2 + r 2 ( p - f ) 2 p 2 f 2 + 2 r h ( p - f ) p 2 f cos α ] 1 2 .
l / t = cos i ,             l / t n = cos ρ ,             sin i / sin ρ = n ,
t n = l / [ 1 - t 2 - l 2 n 2 t 2 ] 1 2 .
Δ E = C · e - μ t n · r d h · d α · d r
T = 0 H α 1 α 2 R 1 R 2 r · e - μ t n · d h · d α · d r 0 H α 1 α 2 R 1 R 2 r · d h · d α · d r .
t n = l [ 1 + 1 2 n 2 · t 2 - l 2 l 2 - 4 n 2 - 3 8 n 4 · ( t 2 - l 2 l 2 ) 2 + ] .
e - μ l 0 H α 1 α 2 R 1 R 2 r · exp [ - μ l 2 n 2 { h 2 p 2 + r 2 ( p - f ) 2 p 2 f 2 + 2 r h ( p - f ) p 2 f cos α } ] · d h · d α · d r .
e - μ l 0 H α 1 α 2 R 1 R 2 r { 1 - μ l 2 n 2 [ h 2 p 2 + r 2 ( p - f ) 2 p 2 f 2 + 2 r h ( p - f ) p 2 f cos α ] + μ 2 l 2 8 n 4 [ h 2 p 2 + r 2 ( p - f ) 2 p 2 f 2 + 2 r h ( p - f ) p 2 f cos α ] 2 } d h · d α · d r .
T = e - μ l { 1 - μ l 2 n 2 p 2 [ H 2 3 + D 2 R ( 4 ) 2 f 2 + 2 A H D R ( 3 ) 3 f ] + μ 2 l 2 4 n 4 p 4 [ H 4 10 + D 4 R ( 6 ) 6 f 4 + H 2 D 2 R ( 4 ) 3 f 2 + A H 3 D R ( 3 ) 3 f + 2 A H D 3 R ( 5 ) 5 f 3 + B H 2 D 2 R ( 4 ) 6 f 2 ] } ,
D = ( p - f ) , A = sin α 2 - sin α 1 α 2 - α 1 , R ( i ) = R 2 i - R 1 i R 2 2 - R 1 2 , B = sin α 2 cos α 2 - sin α 1 cos α 1 α 2 - α 1 .
T = e - μ l { 1 - μ l 2 n 2 p 2 [ H 2 3 + D 2 R 2 2 f 2 ] + μ 2 l 2 4 n 4 p 4 [ H 4 10 + D 4 R 4 6 f 4 + H 2 D 2 R 2 3 f 2 ] } .
T = e - μ l { 1 - μ l K / n 2 }
T = e - μ l { 1 - μ l k / n 2 } ,
P 0 = f { 1 + 2 3 H 2 / R 2 } .
ln T obs = - μ l + ln ( 1 - μ l n 2 k ) = - μ l - [ μ l n 2 k + 1 2 ( μ l k n 2 ) 2 + ] - μ l [ 1 + k n 2 ]
( μ l ) obs = μ l [ 1 + k / n 2 ] .
T = e - μ l [ 1 - μ l k / n 2 ]