Abstract

An interferometric arrangement that automatically compensates for thermal expansion was used to examine the changes in the refractive index of liquid water at 632.8 nm as a function of temperature from 10 to -15 °C. By combining the results of this research with existing data, we calculated the absolute refractive index in the supercooled region with an accuracy ranging from 3 × 10-6 to 1 × 10-5. A direct observation of the refractive-index maximum of water is reported for the first time to our knowledge and found to occur between 0 and 0.1 °C.

© 2002 Optical Society of America

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References

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  1. C. A. Angell, “Supercooled water,” in Water: A Comprehensive Treatise, F. Franks, ed. (Plenum, New York, 1982), Vol. 7, 1.
  2. J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
    [CrossRef]
  3. H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. 63, 318–320 (1973).
    [CrossRef]
  4. B. Richerzhagen, “Interferometer for measuring the absolute refractive index of liquid water as a function of temperature at 1.064 µm,” Appl. Opt. 35, 1650–1653 (1996).
    [CrossRef] [PubMed]
  5. A. R. Harvey, “Determination of the optical constants of thin films in the visible by static dispersive Fourier transform spectroscopy,” Rev. Sci. Instrum. 69, 3649–3658 (1998).
    [CrossRef]
  6. L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–479 (1938).
    [CrossRef]
  7. Ch. Saubade, “Indice de rêfraction de l’eau pure aux basses tempêratures, pour la longeur d’onde de 589.3 Å,” J. Phys. (Paris) 42, 359–366 (1981).
    [CrossRef]
  8. A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
    [CrossRef]
  9. G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, London, 1995), Sect. 2.5.7.

1998 (2)

A. R. Harvey, “Determination of the optical constants of thin films in the visible by static dispersive Fourier transform spectroscopy,” Rev. Sci. Instrum. 69, 3649–3658 (1998).
[CrossRef]

A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
[CrossRef]

1996 (1)

1991 (1)

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

1981 (1)

Ch. Saubade, “Indice de rêfraction de l’eau pure aux basses tempêratures, pour la longeur d’onde de 589.3 Å,” J. Phys. (Paris) 42, 359–366 (1981).
[CrossRef]

1973 (1)

1938 (1)

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–479 (1938).
[CrossRef]

Angell, C. A.

C. A. Angell, “Supercooled water,” in Water: A Comprehensive Treatise, F. Franks, ed. (Plenum, New York, 1982), Vol. 7, 1.

Bose, T. K.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Dobbins, H. M.

Gallagher, J. S.

A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
[CrossRef]

Ge, J.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Harvey, A. H.

A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
[CrossRef]

Harvey, A. R.

A. R. Harvey, “Determination of the optical constants of thin films in the visible by static dispersive Fourier transform spectroscopy,” Rev. Sci. Instrum. 69, 3649–3658 (1998).
[CrossRef]

Kaye, G. W. C.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, London, 1995), Sect. 2.5.7.

Laby, T. H.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, London, 1995), Sect. 2.5.7.

Marteau, Ph.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Orbriot, J.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Peck, E. R.

Richerzhagen, B.

Saubade, Ch.

Ch. Saubade, “Indice de rêfraction de l’eau pure aux basses tempêratures, pour la longeur d’onde de 589.3 Å,” J. Phys. (Paris) 42, 359–366 (1981).
[CrossRef]

Sengers, J. M. H. L.

A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
[CrossRef]

St-Arnaud, J. M.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Taylor, J. K.

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–479 (1938).
[CrossRef]

Tilton, L. W.

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–479 (1938).
[CrossRef]

Appl. Opt. (1)

J. Res. Natl. Bur. Stand. (1)

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–479 (1938).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. (Paris) (1)

Ch. Saubade, “Indice de rêfraction de l’eau pure aux basses tempêratures, pour la longeur d’onde de 589.3 Å,” J. Phys. (Paris) 42, 359–366 (1981).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

A. H. Harvey, J. S. Gallagher, J. M. H. L. Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 27, 761–774 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive index measurements of liquids using two Michelson interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Rev. Sci. Instrum. (1)

A. R. Harvey, “Determination of the optical constants of thin films in the visible by static dispersive Fourier transform spectroscopy,” Rev. Sci. Instrum. 69, 3649–3658 (1998).
[CrossRef]

Other (2)

C. A. Angell, “Supercooled water,” in Water: A Comprehensive Treatise, F. Franks, ed. (Plenum, New York, 1982), Vol. 7, 1.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 16th ed. (Longman, London, 1995), Sect. 2.5.7.

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Figures (6)

Fig. 1
Fig. 1

(a) Conventional Michelson interferometer used as a refractometer. (b) Autocompensating interferometer.

Fig. 2
Fig. 2

Error associated with the measurement of the change in refractive index from both a Michelson refractometer and an autocompensating interferometer.

Fig. 3
Fig. 3

Schematic illustration of the water sample cell and cooling arrangement:(1) body of sample cell, (2) reference mirror, (3) aluminum slab, (4) Peltier coolers, (5) anchoring blade, (6) body of water cooler, (7) optical table.

Fig. 4
Fig. 4

Location of the TMI, determined by the position of the anomalous peak in the intensity and temperature distribution of the fringes.

Fig. 5
Fig. 5

Absolute refractive index of water as a function of temperature. The pair of dashed curves indicates the extreme values from the equation of Harvey et al. 8The error bars for the data from this research are hidden within the data points on the graph.

Fig. 6
Fig. 6

Histogram illustrating the frequency with which the TMI was located in various temperature intervals. The intervals between dashed lines correspond to TMI determinations made from data of the indicated authors at 632.8 nm.

Equations (7)

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

Δ opl = 2 y Δ n T + 2 n T - 1 Δ y ,
Δ opl = 2 y Δ n T + 2 n T - 1 Δ y - 2 Δ x .
Δ opl = 2 y Δ n T + 2 n T - 1 Δ y - 2 n 0 - 1 Δ y .
Δ opl = 2 y Δ n T .
Δ n T = k T 1 ,   T 2 λ 8 y ,
n T 2 = n T 1 + k T 1 ,   T 2 λ 8 y ,
n T = 1.333073 + 5.021 × 10 - 7   T - 2.937   × 10 - 6   T 2 + 5.800 × 10 - 8   T 3 .

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