Abstract

The thermal coefficients of refractive index have been determined for 23 commercial glasses. The interferometric procedure consisted of determining both the change of optical path of each glass with a change of temperature at a given wavelength and set coefficient of linear thermal expansion of the glass for the same temperature range. A relationship for the dispersion of the thermal coefficient of the refractive index has been found. It has also been possible to relate the chemical composition of glass with the thermal coefficient of the refractive index.

© 1969 Optical Society of America

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References

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  1. The term “refractive index” will be shortened to “index” for this paper.
  2. H. Fizeau, Ann. Chim. Phys. 66, 429 (1862); Pogg. Ann. 119, 87, 297 (1863).
  3. C. Pulfrich, Ann. Phys., Chem. 45, 609 (1892).
  4. Jenaer Glaswerk Schott & Gen., Mainz, Catalog 3050/66–67.
  5. J. O. Reed, Ann. Phys. 65, 707 (1898).
    [Crossref]
  6. C. G. Peters, Natl. Bur. Std. (U.S.) Scientific Papers 20, 635 (1926).
    [Crossref]
  7. F. A. Molby, J. Opt. Soc. Am. 39, 600 (1949).
    [Crossref]
  8. L. Prod’homme, Verres Refractaires 10, 267 (1956); Verres Refractaires 11, 351 (1957); Phys. Chem. Glass 1, 119 (1960); Rev. d’Opt. 40, 407 (1961).
  9. F. F. Martens, Verh. Phys. Ges.,  6, 308 (1904).
  10. R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957).
    [Crossref]
  11. L. W. Tilton, J. Res. Natl. Bur. Std. (U. S.) 14, 393 (1935).
    [Crossref]
  12. For example, see G. W. Morey, The Properties of Glass (Reinhold Publ. Corp., New York, 1954), 2nd ed.

1957 (1)

1956 (1)

L. Prod’homme, Verres Refractaires 10, 267 (1956); Verres Refractaires 11, 351 (1957); Phys. Chem. Glass 1, 119 (1960); Rev. d’Opt. 40, 407 (1961).

1949 (1)

1935 (1)

L. W. Tilton, J. Res. Natl. Bur. Std. (U. S.) 14, 393 (1935).
[Crossref]

1926 (1)

C. G. Peters, Natl. Bur. Std. (U.S.) Scientific Papers 20, 635 (1926).
[Crossref]

1904 (1)

F. F. Martens, Verh. Phys. Ges.,  6, 308 (1904).

1898 (1)

J. O. Reed, Ann. Phys. 65, 707 (1898).
[Crossref]

1892 (1)

C. Pulfrich, Ann. Phys., Chem. 45, 609 (1892).

1862 (1)

H. Fizeau, Ann. Chim. Phys. 66, 429 (1862); Pogg. Ann. 119, 87, 297 (1863).

Fizeau, H.

H. Fizeau, Ann. Chim. Phys. 66, 429 (1862); Pogg. Ann. 119, 87, 297 (1863).

Martens, F. F.

F. F. Martens, Verh. Phys. Ges.,  6, 308 (1904).

Molby, F. A.

Morey, G. W.

For example, see G. W. Morey, The Properties of Glass (Reinhold Publ. Corp., New York, 1954), 2nd ed.

Penndorf, R.

Peters, C. G.

C. G. Peters, Natl. Bur. Std. (U.S.) Scientific Papers 20, 635 (1926).
[Crossref]

Prod’homme, L.

L. Prod’homme, Verres Refractaires 10, 267 (1956); Verres Refractaires 11, 351 (1957); Phys. Chem. Glass 1, 119 (1960); Rev. d’Opt. 40, 407 (1961).

Pulfrich, C.

C. Pulfrich, Ann. Phys., Chem. 45, 609 (1892).

Reed, J. O.

J. O. Reed, Ann. Phys. 65, 707 (1898).
[Crossref]

Tilton, L. W.

L. W. Tilton, J. Res. Natl. Bur. Std. (U. S.) 14, 393 (1935).
[Crossref]

Ann. Chim. Phys. (1)

H. Fizeau, Ann. Chim. Phys. 66, 429 (1862); Pogg. Ann. 119, 87, 297 (1863).

Ann. Phys. (1)

J. O. Reed, Ann. Phys. 65, 707 (1898).
[Crossref]

Ann. Phys., Chem. (1)

C. Pulfrich, Ann. Phys., Chem. 45, 609 (1892).

J. Opt. Soc. Am. (2)

J. Res. Natl. Bur. Std. (U. S.) (1)

L. W. Tilton, J. Res. Natl. Bur. Std. (U. S.) 14, 393 (1935).
[Crossref]

Natl. Bur. Std. (U.S.) Scientific Papers (1)

C. G. Peters, Natl. Bur. Std. (U.S.) Scientific Papers 20, 635 (1926).
[Crossref]

Verh. Phys. Ges. (1)

F. F. Martens, Verh. Phys. Ges.,  6, 308 (1904).

Verres Refractaires (1)

L. Prod’homme, Verres Refractaires 10, 267 (1956); Verres Refractaires 11, 351 (1957); Phys. Chem. Glass 1, 119 (1960); Rev. d’Opt. 40, 407 (1961).

Other (3)

The term “refractive index” will be shortened to “index” for this paper.

Jenaer Glaswerk Schott & Gen., Mainz, Catalog 3050/66–67.

For example, see G. W. Morey, The Properties of Glass (Reinhold Publ. Corp., New York, 1954), 2nd ed.

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Figures (8)

Fig. 1
Fig. 1

Vacuum interferometric dilatometer in which interference fringes associated with the interior surfaces of plates A and B drift across the field of view as three samples of the material being tested C expand when heated. The chamber is evacuated by a pumping system at port D and is heated electrically. Temperature is measured by means of a chromel-alumel thermocouple E.

Fig. 2
Fig. 2

Fringe scanner, recording instrument. Collimated light from laser source A illuminates the sample interferometer B, and a small portion of the fringe pattern is monitored by a slit and photodetector C. The recorded output signal passes through maxima and minima as the fringes drift across the slit.

Fig. 3
Fig. 3

Plot of dnλ/dT vs T for five glasses

Fig. 4
Fig. 4

Plot of (dnλ/dt)/(nλ−1) vs 1/λ2 for data from present Investigation (crosses represent temperature range from 25° to 50°C; circles, from 50° to 75°C).

Fig. 5
Fig. 5

Plot of (dnλ/dT)/(nλ−1) vs 1/λ2 for vitreous silica.

Fig. 6
Fig. 6

Plot of (dnλ/dT)/(nλ−1) vs 1/λ2 for BK 7.

Fig. 7
Fig. 7

Plot of (dnλ/dT)/(nλ−1) vs 1/λ2 for seven optical glasses (temperature range from 20° to 40°C).

Fig. 8
Fig. 8

Thermal-coefficient constants of the refractive index vs the reciprocal of field strengths.

Tables (4)

Tables Icon

Table I Calculated temperature dependence of the indices of 34 glasses.

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Table II Temperature dependence relative to standard air.

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Table III Thermal expansion of glasses.

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Table IV Additive factors for calculation of thermal coefficient of refractive index, 20–40°C.

Equations (21)

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P λ = n λ L .
d P λ / d T = L ( d n λ / d T ) + n λ ( d L / d T ) .
α L = L - 1 ( d L / d T ) .
α P λ = P - 1 ( d P λ / d T )
α n λ = n λ - 1 ( d n λ / d T ) .
α P λ = α n λ + α L .
α n λ = α P λ - α L
d n λ / d T = n λ ( α P λ - α L ) .
d n / d T = F ( λ , T , Σ P i ) ,
( n λ - 1 ) / ρ = r ,
d n λ / d T = ( n λ - 1 ) ( φ λ - 3 α L ) ,
φ λ = d n λ / d T n λ - 1 + 3 α L .
d n λ / d T n λ - 1 = k / λ 2 + d n / d T n - 1
n = [ ( ) ] 1 2 ,
n λ - 1 = ( n - 1 ) exp ( k T / λ 2 ) .
n λ = n + ( n - 1 ) k T / λ 2 + ( n - 1 ) k 2 T 2 / 2 λ 4 + .
A = n B = ( n - 1 ) k T C = ( n - 1 ) k 2 T 2 / 2 ,
n λ = A + B / λ 2 + C / λ 4 + ,
α n λ = Σ p i α in λ ,
σ SiO 2 n λ = 1 / 100 [ ( n λ - 1 ) / n λ ] ( k SiO 2 / λ 2 + γ SiO 2 ) ,
γ SiO 2 = d n / d T n - 1 .