Abstract

The following paper gives a discussion of the methods involved in evaluating the oscillator strengths from both the dispersion and absorption equations for liquids. The resulting equations are then applied to a set of infra-red bands on which the absorption and dispersion were measured.

© 1941 Optical Society of America

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References

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  1. J. C. Slater and N. H. Frank, Introduction to Theoretical Physics (McGraw-Hill, New York, 1933), p. 276, 279.
  2. Actually the system must be looked upon as consisting of a number of coupled oscillators representable by a coupled system of linear equations. Such a set can be transformed however to the above form employing normal coordinates.
  3. Handbuch der Physik (1928), Vol.  XX, p. 496.
  4. M. Born, Optik (Julius Springer, Berlin, 1933), p. 478 without assumptions for simplicity.
  5. Handbuch der Physik, Vol. XX, p. 514; Cl. Schaeffer and F. Matossi, Das Ultra Rote Spektrum (Julius Springer, Berlin, 1930), p. 242; J. R. Collins, Phys. Rev. 55, 470 (1939); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
    [CrossRef]
  6. The total refractive index must be used in all these calculations for it is this which determines the velocity of propagation of the wave in the frequency range of the absorption and not that in which the effect of more distant bands has been removed by extrapolation.
  7. K. F. Herzfeld, J. Opt. Soc. Am. 29, 355 (1939).
    [CrossRef]
  8. A. Einstein, Physik. Zeits. 18, 121 (1917).
  9. Theoretically, the better way to proceed is to work with areas as in the absorption case for then a given experimental curve might conceivably be built up by a series of curves of the above form. Such an integration of Eq. (9) involves the evaluation off0=∫ν1ν2n′2dν-∫ν1ν2n02dν∫0∞N∊2/πm′·(ν˜02-ν2)dν(ν˜02-ν2)2+γ2ν2(ν1 and ν2 being outside the region of absorption). The upper two integrals can be evaluated graphically, but the lower, although integrable, is somewhat tedious to handle.
  10. Handbuch der Physik, Vol.  XX (1928); T. Wetterblad, Dissertation, Upsala (1924); H. H. Marvin, Phys. Rev. [1] 34, 161 (1912); A. H. Pfund, J. Opt. Soc. Am. 25, 351, (1935); M. A. Pittman, J. Opt. Soc. Am. 29, 358 (1939); Landolt-Bornstein, Physical Chemistry Tables, Vol. 2 p. 912.
    [CrossRef]
  11. Handbuch der Physik, Vol. XX, p. 499.
  12. F. L. O. Wadsworth, Phil. Mag. p. 348 (1894).
  13. A. H. Pfund, Rev. Sci. Inst. 8, 417 (1937).
    [CrossRef]
  14. R. B. Barnes and F. Matossi, Zeits. f. Physik 76, 24 (1932).
    [CrossRef]
  15. A. H. Pfund, not in print.
  16. G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 43 (1938).
    [CrossRef]
  17. J. Lecomte and J. W. Ellis, Traite de Chimie Organique, Grignard II, pp. 196, 197 (1936).
  18. A. H. Pfund, J. Opt. Soc. Am. 14, 337–338 (1927).
    [CrossRef]
  19. P. E. Shearin and E. K. Plyler, J. Opt. Soc. Am. 28, 61 (1938).
    [CrossRef]
  20. K. W. F. Kohlrausch, Zeits. f. physik. Chemie B28, 340 (1935).
  21. Cl. Schaeffer and F. Matossi, reference 5, p. 266; Con. Corin and G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 48 (1938); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
    [CrossRef]
  22. J. Lecomte, Thesis, Paris, 1924; G. B. Bonino, Gazz. Chim. Ital. 53, 555 (1923); Con. Corin, Comptes rendus 202, 747–749 (1936); J. W. Ellis, Phys. Rev. 23, 48 (1924).
    [CrossRef]

1939 (1)

1938 (2)

G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 43 (1938).
[CrossRef]

P. E. Shearin and E. K. Plyler, J. Opt. Soc. Am. 28, 61 (1938).
[CrossRef]

1937 (1)

A. H. Pfund, Rev. Sci. Inst. 8, 417 (1937).
[CrossRef]

1936 (1)

J. Lecomte and J. W. Ellis, Traite de Chimie Organique, Grignard II, pp. 196, 197 (1936).

1935 (1)

K. W. F. Kohlrausch, Zeits. f. physik. Chemie B28, 340 (1935).

1932 (1)

R. B. Barnes and F. Matossi, Zeits. f. Physik 76, 24 (1932).
[CrossRef]

1928 (2)

Handbuch der Physik, Vol.  XX (1928); T. Wetterblad, Dissertation, Upsala (1924); H. H. Marvin, Phys. Rev. [1] 34, 161 (1912); A. H. Pfund, J. Opt. Soc. Am. 25, 351, (1935); M. A. Pittman, J. Opt. Soc. Am. 29, 358 (1939); Landolt-Bornstein, Physical Chemistry Tables, Vol. 2 p. 912.
[CrossRef]

Handbuch der Physik (1928), Vol.  XX, p. 496.

1927 (1)

1917 (1)

A. Einstein, Physik. Zeits. 18, 121 (1917).

1894 (1)

F. L. O. Wadsworth, Phil. Mag. p. 348 (1894).

Barnes, R. B.

R. B. Barnes and F. Matossi, Zeits. f. Physik 76, 24 (1932).
[CrossRef]

Born, M.

M. Born, Optik (Julius Springer, Berlin, 1933), p. 478 without assumptions for simplicity.

Einstein, A.

A. Einstein, Physik. Zeits. 18, 121 (1917).

Ellis, J. W.

J. Lecomte and J. W. Ellis, Traite de Chimie Organique, Grignard II, pp. 196, 197 (1936).

Frank, N. H.

J. C. Slater and N. H. Frank, Introduction to Theoretical Physics (McGraw-Hill, New York, 1933), p. 276, 279.

Herzfeld, K. F.

Kohlrausch, K. W. F.

K. W. F. Kohlrausch, Zeits. f. physik. Chemie B28, 340 (1935).

Lecomte, J.

J. Lecomte and J. W. Ellis, Traite de Chimie Organique, Grignard II, pp. 196, 197 (1936).

J. Lecomte, Thesis, Paris, 1924; G. B. Bonino, Gazz. Chim. Ital. 53, 555 (1923); Con. Corin, Comptes rendus 202, 747–749 (1936); J. W. Ellis, Phys. Rev. 23, 48 (1924).
[CrossRef]

Matossi, F.

R. B. Barnes and F. Matossi, Zeits. f. Physik 76, 24 (1932).
[CrossRef]

Cl. Schaeffer and F. Matossi, reference 5, p. 266; Con. Corin and G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 48 (1938); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
[CrossRef]

Pfund, A. H.

A. H. Pfund, Rev. Sci. Inst. 8, 417 (1937).
[CrossRef]

A. H. Pfund, J. Opt. Soc. Am. 14, 337–338 (1927).
[CrossRef]

A. H. Pfund, not in print.

Plyler, E. K.

Schaeffer, Cl.

Cl. Schaeffer and F. Matossi, reference 5, p. 266; Con. Corin and G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 48 (1938); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
[CrossRef]

Shearin, P. E.

Slater, J. C.

J. C. Slater and N. H. Frank, Introduction to Theoretical Physics (McGraw-Hill, New York, 1933), p. 276, 279.

Sutherland, G. B. B. M.

G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 43 (1938).
[CrossRef]

Wadsworth, F. L. O.

F. L. O. Wadsworth, Phil. Mag. p. 348 (1894).

Handbuch der Physik (2)

Handbuch der Physik (1928), Vol.  XX, p. 496.

Handbuch der Physik, Vol.  XX (1928); T. Wetterblad, Dissertation, Upsala (1924); H. H. Marvin, Phys. Rev. [1] 34, 161 (1912); A. H. Pfund, J. Opt. Soc. Am. 25, 351, (1935); M. A. Pittman, J. Opt. Soc. Am. 29, 358 (1939); Landolt-Bornstein, Physical Chemistry Tables, Vol. 2 p. 912.
[CrossRef]

J. Opt. Soc. Am. (3)

Phil. Mag. (1)

F. L. O. Wadsworth, Phil. Mag. p. 348 (1894).

Physik. Zeits. (1)

A. Einstein, Physik. Zeits. 18, 121 (1917).

Proc. Roy. Soc. (1)

G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 43 (1938).
[CrossRef]

Rev. Sci. Inst. (1)

A. H. Pfund, Rev. Sci. Inst. 8, 417 (1937).
[CrossRef]

Traite de Chimie Organique (1)

J. Lecomte and J. W. Ellis, Traite de Chimie Organique, Grignard II, pp. 196, 197 (1936).

Zeits. f. Physik (1)

R. B. Barnes and F. Matossi, Zeits. f. Physik 76, 24 (1932).
[CrossRef]

Zeits. f. physik. Chemie (1)

K. W. F. Kohlrausch, Zeits. f. physik. Chemie B28, 340 (1935).

Other (10)

Cl. Schaeffer and F. Matossi, reference 5, p. 266; Con. Corin and G. B. B. M. Sutherland, Proc. Roy. Soc. 165, 48 (1938); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
[CrossRef]

J. Lecomte, Thesis, Paris, 1924; G. B. Bonino, Gazz. Chim. Ital. 53, 555 (1923); Con. Corin, Comptes rendus 202, 747–749 (1936); J. W. Ellis, Phys. Rev. 23, 48 (1924).
[CrossRef]

A. H. Pfund, not in print.

Handbuch der Physik, Vol. XX, p. 499.

Theoretically, the better way to proceed is to work with areas as in the absorption case for then a given experimental curve might conceivably be built up by a series of curves of the above form. Such an integration of Eq. (9) involves the evaluation off0=∫ν1ν2n′2dν-∫ν1ν2n02dν∫0∞N∊2/πm′·(ν˜02-ν2)dν(ν˜02-ν2)2+γ2ν2(ν1 and ν2 being outside the region of absorption). The upper two integrals can be evaluated graphically, but the lower, although integrable, is somewhat tedious to handle.

J. C. Slater and N. H. Frank, Introduction to Theoretical Physics (McGraw-Hill, New York, 1933), p. 276, 279.

Actually the system must be looked upon as consisting of a number of coupled oscillators representable by a coupled system of linear equations. Such a set can be transformed however to the above form employing normal coordinates.

M. Born, Optik (Julius Springer, Berlin, 1933), p. 478 without assumptions for simplicity.

Handbuch der Physik, Vol. XX, p. 514; Cl. Schaeffer and F. Matossi, Das Ultra Rote Spektrum (Julius Springer, Berlin, 1930), p. 242; J. R. Collins, Phys. Rev. 55, 470 (1939); J. J. Fox and A. E. Martin, Proc. Roy. Soc. 167A, 257 (1938).
[CrossRef]

The total refractive index must be used in all these calculations for it is this which determines the velocity of propagation of the wave in the frequency range of the absorption and not that in which the effect of more distant bands has been removed by extrapolation.

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Figures (6)

Fig. 1
Fig. 1

Infra-red dispersion spectrograph.

Fig. 5
Fig. 5

Absorption n2κ vs. frequency. ——CH2Cl2;—·—CH2Br2; ···· CH2l2.

Tables (4)

Tables Icon

Table I Dispersion of CH2Cl2.

Tables Icon

Table II Dispersion of CH2Br2.

Tables Icon

Table III Dispersion of CH2I2

Tables Icon

Table IV Values are in units of 10−5.

Equations (22)

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

m d 2 P / d t 2 + b d P / d t + k P = N 2 ( E 0 e i ω t + 4 π P / 3 ) ,
n 2 = 1 + 4 π N 2 / m ω 0 2 - 4 π N 2 / 3 m - ω 2 + i b ω / m ,
I z = I 0 e - 4 π ν n κ z / c ,
n 2 ( 1 - κ 2 ) = 1 + 0 N 2 f 0 / π m · ( ν ˜ 0 2 - ν 2 ) ( ν ˜ 0 2 - ν 2 ) 2 + ( b 0 ν / 2 π m ) 2 .
2 n 2 κ = 0 N 2 f 0 / π m · ( b 0 ν / 2 π m ) ( ν ˜ 0 2 - ν 2 ) 2 + ( b 0 ν / 2 π m ) 2 ,
f 0 = 2 π m / N 2 · ( 4 ν ˜ 0 2 - γ 2 ) 1 2 0 n 2 κ d ν π / 2 - tan - 1 [ ( γ 2 - 2 ν ˜ 0 2 ) / γ ( 4 ν ˜ 0 2 - γ 2 ) 1 2 ] .
f 0 = 4 ν ˜ 0 m N 2 0 n 2 κ d ν .
f 0 = 4.7791 × 10 - 16 ( M M / ρ ) ν ˜ 0 0 n 2 κ d ν .
n 2 = n 0 2 + A ( ν ˜ 0 2 - ν 2 ) ( ν ˜ 0 2 - ν 2 ) 2 + γ 2 ν 2 .
γ 2 = A ( λ 2 - λ 0 2 ) λ 0 2 ( n 2 - n 0 2 ) - c 2 ( λ 2 - λ 0 2 ) λ 0 4 λ 2 ,
A = c 2 ( λ 1 4 λ 2 2 + λ 2 2 λ 0 4 - λ 2 4 λ 1 2 - λ 0 4 λ 1 2 ) λ 0 2 λ 1 2 λ 2 2 { λ 1 2 - λ 0 2 n 1 2 - n 1 02 - λ 2 2 - λ 0 2 n 2 2 - n 2 02 } .
f 0 = π m c 2 N 2 · ( λ 1 2 - λ 2 2 ) ( 1 / λ 0 2 - λ 0 2 / λ 1 2 λ 2 2 ) λ 1 2 - λ 0 2 n 1 2 - n 1 02 - λ 2 2 - λ 0 2 n 2 2 - n 2 02 .
f 0 = 3.3782 M M ρ · ( λ 1 2 - λ 2 2 ) ( 1 / λ 0 2 - λ 0 2 / λ 1 2 λ 2 2 ) λ 1 2 - λ 0 2 n 1 2 - n 1 02 - λ 2 2 - λ 0 2 n 2 2 - n 2 02 .
T n 2 κ d ν = 1 n 2 κ d ν + 2 n 2 κ d ν + .
f T = f n n
D λ = D Na - 2 ( S Na - S λ ) 424.8 / 4 ,
e - 4 π ν n κ x / c = s 1 ( ν ) 2 T 1 ( ν ) 2 s 2 ( ν ) 2 T 2 ( ν ) 2 · ( I 3 / I 0 ) ( I 3 / I 0 ) ,
κ = - c 4 π ν x n log e T 1 ( ν ) 2 ( I 3 / I 0 ) ( I 3 / I 0 ) .
f 0 = 2.35 × 10 - 3 ( CH 2 Cl 2 ) , f 0 = 2.47 × 10 - 3 ( CH 2 Br 2 ) , f 0 = 2.85 × 10 - 3 ( CH 2 CI 2 ) .
f 0 = 6.81 × 10 - 3 ( CH 2 Cl 2 ) , f 0 = 20.42 × 10 - 3 ( CH 2 Br 2 ) , f 0 = 39.78 × 10 - 3 ( CH 2 CI 2 ) .
f 0 = 2.61 × 10 - 3 ( CHCl 3 ) , f 0 = 6.65 × 10 - 3 ( CHBr 3 ) .
f0=ν1ν2n2dν-ν1ν2n02dν0N2/πm·(ν˜02-ν2)dν(ν˜02-ν2)2+γ2ν2