Abstract

It was previously shown that one constant per element (other than oxygen) sufficed to calculate the refractive indices (for a single wave-length) of a wide variety of silicate glasses from their compositions and densities. It is now shown that with an additional constant per element (other than oxygen) the dispersions in the visible range can be computed. The average deviation between experimental and calculated values for nFnC is about 5 to 8×10−5, in those systems for which the most accurate data are available.

© 1940 Optical Society of America

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References

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  1. M. L. Huggins, J. Opt. Soc. Am. 30, 420, 495 (1940).
    [CrossRef]
  2. R. W. Wood, Physical Optics (Macmillan, New York, third edition, 1934), p. 486.
  3. R. B. Sosman, The Properties of Silica (Reinhold, New York, 1927).
  4. G. W. Morey, The Properties of Glass (Reinhold, New York, 1938).

1940 (1)

Huggins, M. L.

Morey, G. W.

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

Sosman, R. B.

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

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, third edition, 1934), p. 486.

J. Opt. Soc. Am. (1)

Other (3)

R. W. Wood, Physical Optics (Macmillan, New York, third edition, 1934), p. 486.

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

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

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Figures (4)

Fig. 1
Fig. 1

Differences between observed refractive indices for silica glass and those calculated, using Eqs. (2) and (4).

Fig. 2
Fig. 2

Differences between observed refractive indices for silica glass and those calculated, using Eqs. (3) and (5).

Fig. 3
Fig. 3

○ Peddle; × Merwin and Andersen.

Fig. 4
Fig. 4

○ Peddle; × Merwin and Andersen.

Tables (2)

Tables Icon

Table I Constants for use in Eqs. (2) and (4).

Tables Icon

Table II Differences between observed and calculated dispersions.

Equations (19)

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V O = k + b Si + c Si N Si + c M N M
( n λ - 1 ) V O = R O = a M N M ,
( n λ 2 - 1 ) V O = R O = a M N M .
a M , λ = d M g M - 1 / λ 2
a M , λ = d M g M - 1 / λ 2 .
1 n λ - 1 = 2 V O a Si , λ = ( 2 V O d Si ) g Si - ( 2 V O d Si ) ( 1 λ 2 ) .
1 n λ - 1 = 2.228 - 1.666 · 10 - 10 ( 1 λ 2 )
d Si = 16.362 5 · 10 10
g Si = 1.337 3 · 10 10 .
g M = a M , λ 2 / λ 2 2 - a M , λ 1 / λ 1 2 a M , λ 2 - a M , λ 1 .
a M , λ = [ ( n λ - 1 ) V O - a M , λ N M ] / N M ,
a M , F = [ ( n F - 1 ) V O - a Si , F N Si ] / N M ,
a M , C = [ ( n C - 1 ) V O - a Si , C N Si ] / N M ,
d M = a M , D ( g M - 1 / λ D 2 ) ,
d Na = [ ( n F - n C ) V O - d Si N Si ( 1 g Si - 1 / λ F 2 - 1 g Si - 1 / λ C 2 ) N Na ( 1 / λ F 2 - 1 / λ C 2 ) ] ( g Na - 1 λ F 2 ) ( g Na - 1 λ C 2 )
d Na = a Na , D ( g Na - 1 / λ D 2 ) .
g Pb = 0.487 - 0.405 N Pb
and             d Pb = 12.72 - 8.13 N Pb .
n F - n C = ( a M , F - a M , C ) N M / V O .