Abstract

A previously proposed refraction and dispersion equation, containing two empirical constants per component oxide, is improved by the addition, for each component, of a term containing a single new constant (the same for all components) and, for each of the components PbO, CaO, and BaO, of another term containing two additional constants characteristic of the component. Tests of the new equation with experimental data, both for simple (crystalline and vitreous) oxides and for 2-, 3-, and multicomponent glasses, show agreement, practically within the probable error of the experimental data, over the visible range of wave-lengths.

© 1942 Optical Society of America

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References

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  1. M. L. Huggins, J. Opt. Soc. Am. 30, 514 (1940).Certain errors in the figures of this paper may be noted here: Figures 1 and 2 should be interchanged. The decimal points in the numbers in the ordinate scales of these figures should all be moved one place to the left. (The actual agreement is 10 times as good as that indicated.) The ordinates of Figs. 1 and 2 should be labeled nλ(obs.)–nλ(calc); that of Fig. 3 should be labeled 10−10gpb.
    [Crossref]
  2. M. L. Huggins, Ind. Eng. Chem. 32, 1433 (1940).
    [Crossref]
  3. J. C. Young and A. N. Finn, J. Research Nat. Bur. Stand. 25, 759 (1940).
    [Crossref]
  4. M. Herzberger, J. Opt. Soc. Am. 32, 70 (1942).
    [Crossref]
  5. M. L. Huggins, J. Opt. Soc. Am. 30, 495 (1940).
    [Crossref]
  6. M. L. Huggins, J. Opt. Soc. Am. 30, 420 (1940).
    [Crossref]
  7. F. Matossi and H. Bluschke, Zeits. f. Physik 108, 295 (1938).
    [Crossref]
  8. R. B. Sosman, The Properties of Silica (Reinhold, New York, 1927).
  9. G. W. Morey and H. E. Merwin, J. Am. Chem. Soc. 58, 2248 (1936).
    [Crossref]
  10. J. Strong and R. T. Brice, J. Opt. Soc. Am. 25, 207 (1935).
    [Crossref]
  11. J. W. Gifford and W. A. Shenstone, Proc. Roy. Soc. London 73, 201 (1904).
  12. J. W. Gifford, Proc. Roy. Soc. London A84, 193 (1910.)
    [Crossref]
  13. H. Trommsdorff, Die Dispersion Jenaer Gläser im ultravioletten Strahlengebiet, Inaug.-Diss. Jena (1901); see reference 8, pp. 595–6.
  14. J. Engl, Ann. d. Physik [5]  25, 600 (1936).
    [Crossref]
  15. S. B. Hendricks and W. E. Deming, Zeits. f. Krist. A91, 290 (1935).
  16. The experimental data for these glasses, as well as most of the other data we have used, are collected in G. W. Morey, The Properties of Glass (Reinhold, New York, 1938). This book has been invaluable to us in this work.
  17. H. W. Safford, Univ. of Pittsburgh Bulletin, 38 (1942).
  18. Reference 16, p. 393, Table XVI. 14. According to a private communication from Dr. Morey, the headings of the last six columns of this table should be: c − b, d − c, e − d, F − e, g − F, h − g. The + signs indicate a 5 in the next decimal place.
  19. Wülfing, Tscherntak’s Mineralog. pelrog. Mitt. 15, 29, 49 (1896);quoted in Int. Crit. Tables7, 21.
  20. H. E. Merwin, Proc. A. S. T. M. 17(2), 497 (1917).
  21. J. C. Young and A. N. Finn, J. Opt. Soc. Am. 31, 383 (1941).
    [Crossref]
  22. E. Kordes, Zeits. f. physik. Chemie B43, 173 (1939).
  23. Reference 16, p. 389, Table XVI. 12. It may be noted that there are several minor discrepancies between the nD and nF−C values in this table and those in Table XVI. 11 for the same glasses.

1942 (1)

1941 (1)

1940 (5)

1939 (1)

E. Kordes, Zeits. f. physik. Chemie B43, 173 (1939).

1938 (1)

F. Matossi and H. Bluschke, Zeits. f. Physik 108, 295 (1938).
[Crossref]

1936 (2)

G. W. Morey and H. E. Merwin, J. Am. Chem. Soc. 58, 2248 (1936).
[Crossref]

J. Engl, Ann. d. Physik [5]  25, 600 (1936).
[Crossref]

1935 (2)

S. B. Hendricks and W. E. Deming, Zeits. f. Krist. A91, 290 (1935).

J. Strong and R. T. Brice, J. Opt. Soc. Am. 25, 207 (1935).
[Crossref]

1917 (1)

H. E. Merwin, Proc. A. S. T. M. 17(2), 497 (1917).

1910 (1)

J. W. Gifford, Proc. Roy. Soc. London A84, 193 (1910.)
[Crossref]

1904 (1)

J. W. Gifford and W. A. Shenstone, Proc. Roy. Soc. London 73, 201 (1904).

1896 (1)

Wülfing, Tscherntak’s Mineralog. pelrog. Mitt. 15, 29, 49 (1896);quoted in Int. Crit. Tables7, 21.

Bluschke, H.

F. Matossi and H. Bluschke, Zeits. f. Physik 108, 295 (1938).
[Crossref]

Brice, R. T.

Deming, W. E.

S. B. Hendricks and W. E. Deming, Zeits. f. Krist. A91, 290 (1935).

Engl, J.

J. Engl, Ann. d. Physik [5]  25, 600 (1936).
[Crossref]

Finn, A. N.

J. C. Young and A. N. Finn, J. Opt. Soc. Am. 31, 383 (1941).
[Crossref]

J. C. Young and A. N. Finn, J. Research Nat. Bur. Stand. 25, 759 (1940).
[Crossref]

Gifford, J. W.

J. W. Gifford, Proc. Roy. Soc. London A84, 193 (1910.)
[Crossref]

J. W. Gifford and W. A. Shenstone, Proc. Roy. Soc. London 73, 201 (1904).

Hendricks, S. B.

S. B. Hendricks and W. E. Deming, Zeits. f. Krist. A91, 290 (1935).

Herzberger, M.

Huggins, M. L.

Kordes, E.

E. Kordes, Zeits. f. physik. Chemie B43, 173 (1939).

Matossi, F.

F. Matossi and H. Bluschke, Zeits. f. Physik 108, 295 (1938).
[Crossref]

Merwin, H. E.

G. W. Morey and H. E. Merwin, J. Am. Chem. Soc. 58, 2248 (1936).
[Crossref]

H. E. Merwin, Proc. A. S. T. M. 17(2), 497 (1917).

Morey, G. W.

G. W. Morey and H. E. Merwin, J. Am. Chem. Soc. 58, 2248 (1936).
[Crossref]

The experimental data for these glasses, as well as most of the other data we have used, are collected in G. W. Morey, The Properties of Glass (Reinhold, New York, 1938). This book has been invaluable to us in this work.

Safford, H. W.

H. W. Safford, Univ. of Pittsburgh Bulletin, 38 (1942).

Shenstone, W. A.

J. W. Gifford and W. A. Shenstone, Proc. Roy. Soc. London 73, 201 (1904).

Sosman, R. B.

R. B. Sosman, The Properties of Silica (Reinhold, New York, 1927).

Strong, J.

Trommsdorff, H.

H. Trommsdorff, Die Dispersion Jenaer Gläser im ultravioletten Strahlengebiet, Inaug.-Diss. Jena (1901); see reference 8, pp. 595–6.

Wülfing,

Wülfing, Tscherntak’s Mineralog. pelrog. Mitt. 15, 29, 49 (1896);quoted in Int. Crit. Tables7, 21.

Young, J. C.

J. C. Young and A. N. Finn, J. Opt. Soc. Am. 31, 383 (1941).
[Crossref]

J. C. Young and A. N. Finn, J. Research Nat. Bur. Stand. 25, 759 (1940).
[Crossref]

Ann. d. Physik (1)

J. Engl, Ann. d. Physik [5]  25, 600 (1936).
[Crossref]

Ind. Eng. Chem. (1)

M. L. Huggins, Ind. Eng. Chem. 32, 1433 (1940).
[Crossref]

J. Am. Chem. Soc. (1)

G. W. Morey and H. E. Merwin, J. Am. Chem. Soc. 58, 2248 (1936).
[Crossref]

J. Opt. Soc. Am. (6)

J. Research Nat. Bur. Stand. (1)

J. C. Young and A. N. Finn, J. Research Nat. Bur. Stand. 25, 759 (1940).
[Crossref]

Proc. A. S. T. M. (1)

H. E. Merwin, Proc. A. S. T. M. 17(2), 497 (1917).

Proc. Roy. Soc. London (2)

J. W. Gifford and W. A. Shenstone, Proc. Roy. Soc. London 73, 201 (1904).

J. W. Gifford, Proc. Roy. Soc. London A84, 193 (1910.)
[Crossref]

Tscherntak’s Mineralog. pelrog. Mitt. (1)

Wülfing, Tscherntak’s Mineralog. pelrog. Mitt. 15, 29, 49 (1896);quoted in Int. Crit. Tables7, 21.

Zeits. f. Krist. (1)

S. B. Hendricks and W. E. Deming, Zeits. f. Krist. A91, 290 (1935).

Zeits. f. Physik (1)

F. Matossi and H. Bluschke, Zeits. f. Physik 108, 295 (1938).
[Crossref]

Zeits. f. physik. Chemie (1)

E. Kordes, Zeits. f. physik. Chemie B43, 173 (1939).

Other (6)

Reference 16, p. 389, Table XVI. 12. It may be noted that there are several minor discrepancies between the nD and nF−C values in this table and those in Table XVI. 11 for the same glasses.

R. B. Sosman, The Properties of Silica (Reinhold, New York, 1927).

H. Trommsdorff, Die Dispersion Jenaer Gläser im ultravioletten Strahlengebiet, Inaug.-Diss. Jena (1901); see reference 8, pp. 595–6.

The experimental data for these glasses, as well as most of the other data we have used, are collected in G. W. Morey, The Properties of Glass (Reinhold, New York, 1938). This book has been invaluable to us in this work.

H. W. Safford, Univ. of Pittsburgh Bulletin, 38 (1942).

Reference 16, p. 393, Table XVI. 14. According to a private communication from Dr. Morey, the headings of the last six columns of this table should be: c − b, d − c, e − d, F − e, g − F, h − g. The + signs indicate a 5 in the next decimal place.

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Figures (20)

F. 1
F. 1

To show agreement with Eqs. (11) and (12) for vitreous silica. The dots represent the most probable refractive index values, according to Sosman (reference 8).

F. 2
F. 2

To show agreement with Eqs. (11) and (12) for quartz. The dots represent mean indices of refraction, computed by means of Eq. (25) from Sosman’s (reference 8) most probable values for the ordinary and extraordinary rays.

F. 3
F. 3

To show agreement with Eqs. (11) and (12) for vitreous B2O3. The dots represent experimental refractive indices by Morey and Merwin (reference 9).

F. 4
F. 4

To show agreement with Eqs. (11) and (12) for crystalline MgO. Experimental data by Strong and Brice (reference 10).

F. 5
F. 5

Differences between observed and calculated indices of refraction for vitreous silica. The “observed” indices are Sosman’s “most probable” values (reference 8). HSD josa-32-11-635-i001 Huggins, Sun, and Davis, Eqs. (1), (22), and (12); H — — — — — Huggins, Eqs. (1) and (5); YF – – – – – – – – Young and Finn, Eq. (23); E ---------------- Engl, Eq. (24); Hb –·–·–·–·–·– Herzberger, Eqs. (13)(17).

F. 6
F. 6

Differences between experimental and calculated mean refractive indices for quartz. HSD josa-32-11-635-i001 Huggins, Sun, and Davis; dSi, Q = 1829.29 · 108; gSi, Q = 149.819 ·108; Hb —·—·—·—· Herzberger.

F. 7
F. 7

Differences between experimental and calculated refractive indices for vitreous B2O3. HSD josa-32-11-635-i001 Huggins, Sun, and Davis; dB″ = 1066.0 ·108; gB″ = 123.752 ·108; Hb —·—·—·—· Herzberger.

F. 8
F. 8

Differences between observed and calculated indices of refraction for crystalline MgO.HSD josa-32-11-635-i001 Huggins, Sun, and Davis; dMg = 912.26 108; gMg= 111.55·108; Hb —·—·—·—·Herzberger.

F. 9
F. 9

Variation of RB′,D (= aB′, DNB′) with NB′ + Ordnance Dept. Document 2037, Superintendent of Documents, Washington, D. C. (1921); ○ Chance Brothers; × Parra-Mantois; ● Turner and co-workers.

F. 10
F. 10

Variation of RB′,FC(= aB′,FCNB′) with NB′. + Ordnance Dept. Document 2037, Superintendent of Documents, Washington, D. C. (1921); ○ Chance Brothers; × Parra-Mantois.

F. 11
F. 11

Variation of RB″,D with NB″. + Wulff and Majumdar (Na2O – B2O3 glasses); ○ Merwin and Morey (B2O3 and unannealed B2O3–SiO2 glasses); ● English and Turner (Na2O–B2O3–SiO2).

F. 12
F. 12

Variation of RB″,FC with NB″ Data by Merwin and Morey on B2O3 and unannealed B2O3–SiO2 glasses.

F. 13
F. 13

Variation of aCa,D with NCa. Data on Na2O – CaO – SiO2 glasses by Morey and Merwin. To avoid confusion, only half of the experimental points are shown.

F. 14
F. 14

Variation of aCa, FC with NCa. Data on Na2O – CaO – SiO2 glasses by Morey and Merwin. Only half of the experimental points are shown.

F. 15
F. 15

Variation of aBa,D with NBa. + Ordnance Dept. Document 2037, Superintendent of Documents, Washington, D. C. (1921); ○ Peddle. Points are omitted for a few glasses of low barium content, which would fall outside the range of aBa, D covered by the figure.

F. 16
F. 16

Variation of aBa, FC with NBa, + Ordnance Dept. Document 2037, Superintendent of Documents, Washington, D. C. (1921); ○ Peddle. A few points are omitted, as for Fig. 15.

F. 17
F. 17

Variation of aPb.λ with NPb, for four wavelengths. Experimental data by Merwin and Andersen (reference 16) on glasses in the Na2O –PbO –SiO2 system. The curves represent Eqs. (3840).

F. 18
F. 18

Variation of aAI,D with NAI. ○ Faick, Young, Hubbard, and Finn; × Larsen (reference 16); ● Safford (reference 17).

F. 19
F. 19

To show agreement with Eqs. (11) and (12) for hematite (Fe2O3) crystals. ○ Wülfing (reference 19); × Merwin (reference 20).

F. 20, 21, and 22
F. 20, 21, and 22

To show agreement between observed dispersion data and various empirical equations, for certain analyzed glasses. 1 josa-32-11-635-i002 Huggins, Sun, and Davis, using experimental nD and nFnC; 2 josa-32-11-635-i003 Huggins, Sun, and Davis, using experimental nD; 3 josa-32-11-635-i001 Huggins, Sun, and Davis, using experimental ρ; 4 ———— Huggins, Sun, and Davis, using calculated ρ; H; —;—;—;— Huggins, using experimental ρ; YF – – – – – – – Young and Finn, using experimental ρ; Hb — · — · — · Herzberger, using experimental nD and nFnC. Figure 20 (upper left) is for a Na2O–SiO2 glass (No. 132); Fig. 21 (upper right), for a CaO — SiO2 glass (No. 139); and Fig. 22 (lower right), for a Na2O –CaO – SiO2 glass (No. 98).

Tables (3)

Tables Icon

Table I Rough values of the ratio dM,i/dM, using dM,i values computed from Eq. (21).

Tables Icon

Table II Characteristic refraction and dispersion constants.

Tables Icon

Table III Comparisons of observed and calculated refractive indices and dispersions for certain analyzed glasses.

Equations (58)

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µ λ = n λ 1 = R 0 , λ / V 0 = R M , λ / V 0 = a M , λ N M / V 0 ,
V 0 = [ ρ ( n M f M / W M ) ] 1 .
V 0 = k + b Si + c Si N Si + c M N M ,
N M = m M f M / W M ( n M f M / W M ) .
a M , λ = d M g M ( 1 / λ 2 ) ,
g M = 1 / λ M 2 .
a M , λ = d M 1 / λ M 2 1 / λ 2 + d M , i 1 / λ M , i 2 1 / λ 2 .
λ M , i λ
d M , i 1 / λ M , i 2 1 / λ 2 d M , i λ 2 .
a M , λ = d M g M 1 / λ 2 d M , i λ 2 .
1 a M , λ + d M , i λ 2 = g M d M 1 d M λ 2 .
d M , i / d M = k i = 48 10 6 ,
µ λ = K + K λ 2 + K λ 2 λ 1 2 + K ( λ 2 λ 1 2 ) 2 ,
K = α µ D + α ( µ F µ C ) ,
K = β µ D + β ( µ F µ C ) ,
K = γ µ D + γ ( µ F µ C ) ,
K = δ µ D + δ ( µ F µ C ) ,
a M , λ = k M + k M λ 2 + k M λ 2 λ 1 2 + k M ( λ 2 λ 1 2 ) 2 ,
k M = α a D + α a F C ,
k M = β a D + β a F C ,
d M , i k M = 70.58 10 4 a D 889 10 4 a F C .
a M , λ = d M g M 1 / λ 2 k i d M λ 2 ,
n λ 1 ρ = 100 f M ( α M + β M λ 2 ) ,
n λ 2 1 n λ 2 + 2 = A a c 2 / λ 2 + B b c 2 / λ 2 ,
n ¯ = ( 2 n ω 2 + n 2 3 ) 1 2
1 a Si , λ + k i [ d Si ] λ 2 [ g Si ] [ d Si ] + 1 [ d Si ] λ 2
R Na , D = µ D V 0 R Si , D = µ D V 0 a Si , D N Si
R Na , F C = ( µ F µ C ) V 0 R Si , F C = ( µ F µ C ) V 0 a Si , F C N Si .
a Na , D = R Na , D / N Na
a Na , F C = R Na , F C / N Na .
R M , D = µ D V 0 a M , D N M ,
g M = [ a M , λ 1 / λ 1 2 a M , λ 2 / λ 2 2 a M , λ 1 a M , λ 2 ] ϕ ,
ϕ = 1 + k i k i λ 1 2 g M 1 + k i k i λ 2 2 g M .
θ g M 2 + ( ϕ θ λ C 2 ϕ + θ λ F 2 ) g M + ( θ λ F 2 λ C 2 + ϕ λ D 2 λ F 2 ϕ λ D 2 λ C 2 ) = 0
ϕ = 1 k i ( λ F 2 λ C 2 ) / ( 1 g M 1 / λ F 2 1 g M 1 / λ C 2 ) 1 k i λ D 2 ( g M 1 / λ D 2 ) .
N B = N B N B = 0 .
N B = 2 4 N Si 3 N B N B = 4 N Si + 4 N B 2 .
a M , λ = a M , λ ° + a M , λ N M
a Pb , λ = a Pb , λ ° + a Pb , λ N Pb 2 .
a Pb , λ ° = d Pb ° g Pb ° 1 / λ 2 k i d Pb ° λ 2
a Pb , λ = d Pb g Pb 1 / λ 2 .
( n D 1 ) / ρ = r M , D f M
n F C / ρ = ( n F n C ) / ρ = r M , F C f M .
a M , D = r M , D W M / m M
a M , F C = r M , F C W M / m M .
µ λ = α A λ β B λ ,
A λ = M d M N M g M 1 / λ 2 + Ca , Ba d M N M 2 g M 1 / λ 2 + d Pb N Pb 3 g Pb 1 / λ 2 ,
B λ = λ 2 d M N M ,
α = λ 2 2 µ λ 1 λ 1 2 µ λ 2 λ 2 2 A λ 1 λ 1 2 A λ 2
β = A λ 2 µ λ 1 A λ 1 µ λ 2 A λ 1 B λ 2 A λ 2 B λ 1 .
α = ( λ F 2 λ C 2 ) µ D λ D 2 ( µ F µ C ) ( λ F 2 λ C 2 ) A D λ D 2 ( A F A C )
β = ( A F A C ) µ D A D ( µ F µ C ) A D ( B F B C ) ( A F A C ) B D .
a F C ° = 0.260
a F C = 0.04
a F C ° = 0.34
a F C = 0.7
a F C ° = 1.30
a F C = 5.61