Abstract

The refraction per gram atom of oxygen, defined by a formula of either the Gladstone-Dale, the Newton, or the Lorentz-Lorenz type, equals the sum of terms characteristic of the component “metallic” elements, each of these terms being proportional to the number of atoms of that element per atom of oxygen. This is shown to be true (with but little error) for practically all classes of silicate glasses for which adequate data are available for testing the relationship. (Deviations from strict proportionality are, however, observed for glasses containing large amounts of lead.) Constants are derived empirically for use in the Gladstone-Dale and Newton type equations. Different constants are needed for triangularly surrounded and for tetrahedrally surrounded boron atoms. Using the equations previously derived for the calculation of the density and volume per oxygen, it is now possible to compute the refractive index (for the sodium D lines) of a wide variety of silicate glasses from the composition alone.

© 1940 Optical Society of America

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References

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  1. M. L. Huggins, J. Opt. Soc. 30, 420 (1940).
    [CrossRef]
  2. J. H. Gladstone and T. P. Dale, Trans. Roy. Soc. (London) 153, 317, 337 (1863).
  3. H. A. Lorentz, Ann. d. Physik 9, 641 (1880).
    [CrossRef]
  4. L. Lorenz, Ann. d. Physik 11, 70 (1880).
    [CrossRef]
  5. S. S. Kurtz and A. L. Ward, J. Frank. Inst. 222, 563 (1936); J. Frank. Inst. 224, 583 (1937).
    [CrossRef]
  6. Isaac Newton, Opticks Book  II (1717). See reference 5.
  7. R. W. Wood, Physical Optics (Macmillan, New York, 1934).
  8. J. F. Eykman, Rec. trav. chim. 14, 185, 201 (1895).
    [CrossRef]
  9. K. Lichtenecker, Physik. Zeits. 27, 115, 833 (1926).
  10. G. W. Morey and H. E. Merwin, J. Opt. Soc. 22, 632 (1932).
    [CrossRef]
  11. G. W. Morey, The Properties of Glass (Reinhold, New York, 1938).
  12. C. A. Faick and A. N. Finn, J. Am. Ceram. Soc. 14, 518 (1931).
    [CrossRef]

1940 (1)

M. L. Huggins, J. Opt. Soc. 30, 420 (1940).
[CrossRef]

1936 (1)

S. S. Kurtz and A. L. Ward, J. Frank. Inst. 222, 563 (1936); J. Frank. Inst. 224, 583 (1937).
[CrossRef]

1932 (1)

G. W. Morey and H. E. Merwin, J. Opt. Soc. 22, 632 (1932).
[CrossRef]

1931 (1)

C. A. Faick and A. N. Finn, J. Am. Ceram. Soc. 14, 518 (1931).
[CrossRef]

1926 (1)

K. Lichtenecker, Physik. Zeits. 27, 115, 833 (1926).

1895 (1)

J. F. Eykman, Rec. trav. chim. 14, 185, 201 (1895).
[CrossRef]

1880 (2)

H. A. Lorentz, Ann. d. Physik 9, 641 (1880).
[CrossRef]

L. Lorenz, Ann. d. Physik 11, 70 (1880).
[CrossRef]

1863 (1)

J. H. Gladstone and T. P. Dale, Trans. Roy. Soc. (London) 153, 317, 337 (1863).

1717 (1)

Isaac Newton, Opticks Book  II (1717). See reference 5.

Dale, T. P.

J. H. Gladstone and T. P. Dale, Trans. Roy. Soc. (London) 153, 317, 337 (1863).

Eykman, J. F.

J. F. Eykman, Rec. trav. chim. 14, 185, 201 (1895).
[CrossRef]

Faick, C. A.

C. A. Faick and A. N. Finn, J. Am. Ceram. Soc. 14, 518 (1931).
[CrossRef]

Finn, A. N.

C. A. Faick and A. N. Finn, J. Am. Ceram. Soc. 14, 518 (1931).
[CrossRef]

Gladstone, J. H.

J. H. Gladstone and T. P. Dale, Trans. Roy. Soc. (London) 153, 317, 337 (1863).

Huggins, M. L.

M. L. Huggins, J. Opt. Soc. 30, 420 (1940).
[CrossRef]

Kurtz, S. S.

S. S. Kurtz and A. L. Ward, J. Frank. Inst. 222, 563 (1936); J. Frank. Inst. 224, 583 (1937).
[CrossRef]

Lichtenecker, K.

K. Lichtenecker, Physik. Zeits. 27, 115, 833 (1926).

Lorentz, H. A.

H. A. Lorentz, Ann. d. Physik 9, 641 (1880).
[CrossRef]

Lorenz, L.

L. Lorenz, Ann. d. Physik 11, 70 (1880).
[CrossRef]

Merwin, H. E.

G. W. Morey and H. E. Merwin, J. Opt. Soc. 22, 632 (1932).
[CrossRef]

Morey, G. W.

G. W. Morey and H. E. Merwin, J. Opt. Soc. 22, 632 (1932).
[CrossRef]

G. W. Morey, The Properties of Glass (Reinhold, New York, 1938).

Newton, Isaac

Isaac Newton, Opticks Book  II (1717). See reference 5.

Ward, A. L.

S. S. Kurtz and A. L. Ward, J. Frank. Inst. 222, 563 (1936); J. Frank. Inst. 224, 583 (1937).
[CrossRef]

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1934).

Ann. d. Physik (2)

H. A. Lorentz, Ann. d. Physik 9, 641 (1880).
[CrossRef]

L. Lorenz, Ann. d. Physik 11, 70 (1880).
[CrossRef]

J. Am. Ceram. Soc. (1)

C. A. Faick and A. N. Finn, J. Am. Ceram. Soc. 14, 518 (1931).
[CrossRef]

J. Frank. Inst. (1)

S. S. Kurtz and A. L. Ward, J. Frank. Inst. 222, 563 (1936); J. Frank. Inst. 224, 583 (1937).
[CrossRef]

J. Opt. Soc. (2)

M. L. Huggins, J. Opt. Soc. 30, 420 (1940).
[CrossRef]

G. W. Morey and H. E. Merwin, J. Opt. Soc. 22, 632 (1932).
[CrossRef]

Opticks (1)

Isaac Newton, Opticks Book  II (1717). See reference 5.

Physik. Zeits. (1)

K. Lichtenecker, Physik. Zeits. 27, 115, 833 (1926).

Rec. trav. chim. (1)

J. F. Eykman, Rec. trav. chim. 14, 185, 201 (1895).
[CrossRef]

Trans. Roy. Soc. (London) (1)

J. H. Gladstone and T. P. Dale, Trans. Roy. Soc. (London) 153, 317, 337 (1863).

Other (2)

R. W. Wood, Physical Optics (Macmillan, New York, 1934).

G. W. Morey, The Properties of Glass (Reinhold, New York, 1938).

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Figures (26)

Fig. 1
Fig. 1

Na2O-SiO2. O Faick and Finn;×Morey and Merwin. RO=6.255 + 2.878NNa.

Fig. 2
Fig. 2

Na2O-SiO2 (Peddle). RO, Na=6.0NNa.

Fig. 3
Fig. 3

□ CaO-SiO2;×Na2O-CaO-SiO2 (Morey and Merwin). RO, Ca=12.64NCa.

Fig. 4
Fig. 4

Na2O-CaO-SiO2 (Faick and Finn). RO, Ca=12.55NCa.

Fig. 5
Fig. 5

Na2O-CaO-SiO2 (-MgO-Al2O3-Fe2O3) (English and Turner). RO, Ca=12.55NCa.

Fig. 6
Fig. 6

● Na2O-CaO-SiO2;×K2O-CaO-SiO2; ○ Na2O-K2O-CaO-SiO2 (Peddle). RO, Ca=12.55 NCa.

Fig. 7
Fig. 7

□ K2O-SiO2;×K2O-CaO-SiO2 (Merwin and Morey). RO, K=9.53NK.

Fig. 8
Fig. 8

Na2O-K2O-CaO-B2O3-SiO2(-Al2O3-Fe2O3) (Turner and Winks). RO, K=9.5NK.

Fig. 9
Fig. 9

□ K2O-SiO2; ● K2O-CaO-SiO2; ○ Na2O-K2O-CaO-SiO2 (Peddle). RO, K=9.5NK.

Fig. 10
Fig. 10

Li2O-SiO2 (Kracek). RO, Li=4.4NLi.

Fig. 11
Fig. 11

Na2O-BeO-SiO2(-CaO-Al2O3-Fe2O3).×series A and V; ● series P (Becker). RO, Be=5.9NBe.

Fig. 12
Fig. 12

● Na2O-BeO-SiO2; ○ K2O-BeO-SiO2 (Lai and Silverman). RO, Be=5.9 NBe.

Fig. 13
Fig. 13

MgO-CaO-SiO2 (Larsen). RO, Mg=8.6 NMg.

Fig. 14
Fig. 14

SrO-SiO2 (Eskola). RO, Sr=16NSr.

Fig. 15
Fig. 15

● Na2O-BaO-SiO2; ○ K2O-BaO-SiO2;×Na2O-K2O-BaO-SiO2 (Peddle). RO, Ba=20.5 NBa.

Fig. 16
Fig. 16

Na2O-ZnO-SiO2(-CaO-Al2O3-Fe2O3) (English, Turner and Winks). RO, Zn=12.2NZn.

Fig. 17
Fig. 17

×Na2O-PbO-SiO2; □ Na2O-K2O-PbO-SiO2 (Merwin and Andersen). RO, Pb=30NPb for small NPb.

Fig. 18
Fig. 18

Na2O-PbO-SiO2; ○ K2O-PbO-SiO2;×Na2O-K2O-PbO-SiO2 (Peddle). RO, Pb≈30NPb for small NPb.

Fig. 19
Fig. 19

● Na2O-B2O3-SiO2(-CaO-Al2O3-Fe2O3); ○ Na2O-K2O-CaO-B2O3-SiO2(-Al2O3-Fe2O3) (English and Turner). RO, B′=7.8NB′.

Fig. 20
Fig. 20

Na2O-B2O3-SiO2(-CaO-Al2O3-Fe2O3) (English and Turner). RO, B′=8.8NB″.

Fig. 21
Fig. 21

Na2O-Al2O3-SiO2 (Faick, Young, Hubbard and Finn). RO, Al=10.45NAl.

Fig. 22
Fig. 22

Na2O-Al2O3-SiO2(-CaO-Fe2O3) (English and Turner). RO, A1=10.5NAl.

Fig. 23
Fig. 23

Na2O-CaO-Al2O3-SiO2 (Larsen). RO, Al=10.5NAl.

Fig. 24
Fig. 24

Na2O-Fe2O3-SiO2 (Bowen, Schairer and Willems). RO, Fe=23NFe.

Fig. 25
Fig. 25

Na2O-Bi2O3-SiO2 (Riegel and Sharp). RO, Bi=34NBi.

Fig. 26
Fig. 26

Na2O-TiO2-SiO2(-CaO-Al2O3-Fe2O3) (Sheen and Turner). RO, Ti=25NTi.

Tables (4)

Tables Icon

Table I Average deviations between observed and calculated refractions and indices of refraction for sodium silicate glasses.

Tables Icon

Table II Values of aM for use in Eq. (4).

Tables Icon

Table III Values of aM for use in Eq. (8).

Tables Icon

Table IV Comparison of refraction constants for silicate glasses and for oxide crystals.

Equations (22)

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V O = k + b Si + c Si N Si + c M N M ,
V O = 1 ρ n M f M / W M
N M = m M f M / W M n M f M / W M .
R O = R O , M = a M N M .
R O = ( n D - 1 ) V O = n D - 1 ρ n M f M / W M .
R O = ( n D 2 - 1 n D 2 + 2 ) V O = ( n D 2 - 1 ) / ( n D 2 + 2 ) ρ n M f M / W M .
R O = ( n D 2 - 1 ) V O = n D 2 - 1 ρ n M f M / W M .
R O = R O , M = a M N M .
Morey and Merwin : R O = 6.253 + 2.892 N Na ,
Faick and Finn :         R O = 6.265 + 2.844 N Na .
n M m M N M = 1 ,
R O = a M ( G ) N M = a M ( B ) N M .
a M ( G ) - a M ( B ) = ( a M ( B ) - a M ( G ) ) N M N M ,
a M ( G ) - a M ( B ) = ( a Si ( B ) - a Si ( G ) ) N Si N M .
ν M N M = 2 ,
N Si = 1 2 - ν M 4 N M .
a M ( G ) - a M ( B ) = ( a Si ( B ) - a Si ( G ) ) ( 1 2 N M - ν M 4 )
= 0.024 ( 1 2 N M - ν M 4 ) = 0.012 N M - 0.006 ν M .
n D = 1 + a M N M V O = 1 + ρ a M N M · n M f M W M .
n D 2 = 1 + a M N M V O = 1 + ρ a M N M · n M f M W M .
n D = 1 + a M N M k + b Si + c Si N Si + c M N M ,
n D 2 = 1 + a M N M k + b Si + c Si N Si + c M N M ,