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Refractive index of water | Table of contents |
▶ Refractive index of water
▶ Refractive index of water, complex
▶ Refractive index of water, complex, real part
▶ Refractive index of water, complex
▶ Refractive index of water, complex, data
▶ Refractive index of water, complex, imaginary part
▶ Refractive index of water, complex, imaginary part, data
▶ Refractive index of water, complex, Kramers-Krönig analysis
▶ Refractive index of water, complex, models
▶ Refractive index of water, complex, real part
▶ Refractive index of water, complex, real part, data
▶ Refractive index of water, complex, real part, formulas
▶ Refractive index of water, reviews
■ Refractive index of seawater
Refractive index of water, complex
▶ Refractive index of water, complex, data
▶ Refractive index of water, complex, imaginary part
▶ Refractive index of water, complex, models
▶ Refractive index of water, complex, real part
■ Refractive index of seawater, complex
Refractive index of water, complex, data
wavelength 10 nm to 10 m, Kramers-Krönig analysis: Querry MR et al 1991
wavelength 12.4 nm to 1.2 μm, inelastic x-ray scattering: Hayashi Hisashi and Nozomu 2015
wavelength 83.2 nm to 125.2 nm (14.9 to 9.9 eV), complex dielectric function: Kerr GD et al 1972
wavelength 105 nm to 300 nm: Painter LR et al 1969
wavelength 200 nm to 200 μm, Kramers-Krönig analysis: Hale GM and Querry 1973
wavelength 200 nm to 200 μm, compiled data: Irvine WM and Pollack 1968
wavelength 360 nm to 2.362 μm, temperature 27 °C: Palmer KF and Williams 1974
wavelength 514.5 nm, temperature 1000 K and 2000 K, pressure 0 to 30 GPa, molecular dynamics calculations: Pan Ding et al 2014
Molecular dynamics calculations by Pan Ding et al 2014 indicate, in agreement with experimental results of Sanchez-Valle C et al 2013 at 673 K, that the refractive index and electronic bandgap of water and ice increase with pressure (at least up to 30 GPa) - a behavior contrary to that observed for many other materials. This result (for ice) is consistent with those of Hermann A and Schwerdtfeger 2011 obtained via many body perturbation theory. The latter results are also consistent with a blueshift of the optical absorption spectrum when water vapor condenses into liquid [Hermann A et al 2008; see also Absorption coefficient of water, ordinary (H_{2}O), phase changes].
wavelength 667 nm to 10 mm (15000 to 1 cm^{-1}), temperature 25 °C: Bertie JE and Lan 1996
wavelength 2 μm to 30.3 μm: Rusk AN et al 1971
wavelength 1.67 μm to DC (6000 to 0 cm^{-1}), attenuated total reflection method: Max JJ and Chapados 2009
wavelength 2 μm to 1 mm, temperature 27 °C, Kramers-Krönig analysis: Downing HD and Williams 1974
wavelength 2 μm to 25 μm (5000 to 400 cm^{-1}), temperature 1, 16, 39, and 50 °C : Pinkley LW et al 1976
wavelength 2.22 μm to 9.09 μm (4500 cm^{-1} to 1100 cm^{-1}), temperature 269 K, 258 K, 252 K, and 238 K (supercooled water), light scattering by water droplets and Kramers-Krönig analysis: Wagner R et al 2005
wavelength 2.5 to 21.74 μm (4000 to 460 cm^{-1}), temperature 240, 253, 263, and 273 K (supercooled water): Zasetsky AY et al 2005
wavelength 3 μm to 12.5 μm: Deibler LL and Smith 2001
wavelength 22.2 μm to 400 μm, -5.6 °C ≤ t ≤ 81.4 °C: Zelsman HR 1995
wavelength 22.2 μm to 1667 μm (450 to 6 cm^{-1}), temperature 19 °C, real part of the complex refractive index and absorption coefficient: Afsar MN and Hasted 1977
wavelength 45.4 μm to 2000 μm (220 to 5 cm^{-1}), temperature 4, 30, 57 °C, real part of the complex refractive index and absorption coefficient: Afsar MN and Hasted 1978
wavelength 1 mm to 6 mm, real part of the refractive index and absorption coefficient: Czumaj Z 1990
wavelength 9 mm to DC (static), molecular dynamics calculations, complex dielectric function: Abeyrathne CD et al 2013
wavelength 32 mm (~9.35 GHz), temperature 0 to 10 °C: van Kalleveen THT and Buckmaster 1988
wavelength 32 mm (~9.35 GHz), temperature 10 °C to 40 °C: Zaghloul H and Buckmaster 1985
wavelength 99 mm to 2.997 m (3 to 0.1 GHz), complex dielectric function: Schwan HP et al 1976
◀ Refractive index of water, complex
■ Refractive index of water, complex, imaginary part, data
■ Refractive index of water, complex, real part, data
■ Refractive index of seawater, complex, data
■ Refractive index, complex, and dielectric function
■ Absorption coefficient of water
Refractive index of water, complex, imaginary part
▶ Refractive index of water, complex, imaginary part, data
◀ Refractive index of water, complex
■ Refractive index of water, complex, real part
■ Refractive index, complex, imaginary part
■ Absorption coefficient of water
Refractive index of water, complex, imaginary part, data
For data on the real and imaginary parts of the complex refractive index of water, please see Refractive index of water, complex, data. The imaginary part of the complex refractive index of water, m", is related to the absorption coefficient by Eq. 2 in Refractive index, complex, imaginary part, and absorption of light. Hence, for data specifically on m" (expressed as the absorption coefficient), you can also see Absorption coefficient of water, ordinary (H_{2}O), data.
◀ Refractive index of water, complex, imaginary part
■ Refractive index of water, complex, data
■ Refractive index of water, complex, real part, data
■ Absorption coefficient of water
Refractive index of water, complex, Kramers-Krönig analysis
wavelength 10 nm to 10 m: Querry MR et al 1991
wavelength 2 μm to 1 mm, temperature 27 °C: Downing HD and Williams 1974
◀ Refractive index of water, complex
Refractive index of water, complex, models
Pressure dependence model of the real part of the complex refractive index based on mixed-bonding structural model of water (Cho CH et al 2001a) yields better than 5-decimal-point agreement with experimental refractive index data at discrete wavelengths in the visible and at low pressures and temperatures between about -10 °C and 70 °C.
Temperature dependence model:
temperature -10 °C to +70 °C, real part of the complex refractive index: Cho CH et al 2001a,
temperature 0 to 100 °C; wavelength 200 nm to 800 nm, temperature 0 to 100°C, real part of the complex refractive index: Djurišić AB and Stanić 1999.
Wavelength dependence model:
wavelength 30 nm to 3 m: Shubitidze F and Österberg 2007
wavelength 200 nm to 200 μm, temperature 25°C: Djurišić AB and Stanić 1998
wavelength 2 μm to ~1 m, temperature -20 to 50 °C: Ray PS 1972.
◀ Refractive index of water, complex
■ Refractive index of seawater, complex, real part, models
Refractive index of water, complex, real part
▶ Refractive index of water, complex, real part, data
▶ Refractive index of water, complex, real part, formulas
◀ Refractive index of water, complex
■ Refractive index of water, complex, imaginary part
■ Refractive index, complex, real part
■ Refractive index of seawater, complex, real part
Refractive index of water, complex, real part, data
For data on the real and imaginary parts of the complex refractive index of water, please see Refractive index of water, complex, data. The following list contains references specifically on the real part, m', of the complex refractive index of water.
wavelength 190 nm to 1129 nm, temperature 19 °C, 21.5 °C, and 24 °C, minimum deviation method: Daimon M and Masumura 2007
wavelength ~191 nm to ~560 nm, temperature 21.5 °C, minimum deviation method, interferometry: Burnett JH and Kaplan 2004
wavelength 193 nm, 248 nm, 633 nm, temperature 0 °C to 50 °C, effect of dissolved air, laser-based refractometer: Harvey AH et al 2005
wavelength 405 nm to 707 nm, temperature 0 °C to 60 °C: Tilton LW and Taylor 1938 (minimum deviation method, see also comments on high accuracy of these data in Millard RC and Seaver 1990)
wavelength 467.8 nm to 667.8 nm; temperature 7.64 °C to 24.8 °C, pressure 1 b to 1108 b, interferometry: Waxler RM et al 1964 (see also comments on modifications of these data by others in Millard RC and Seaver 1990)
wavelength 514.5 nm, temperature 293 K to 673 K, pressure 0 to 5.62 GPa, density dependence: Sanchez-Valle C et al 2013
wavelength 532 nm to 633 nm, temperature 23 °C, pressure ambient to 250 MPa, interferometry: Weiss L et al 2012
wavelength 587.6 nm, temperature 1.56 °C, 7.64 °C, 24.80 °C, 34.50 °C, 54.34 °C, pressure 0.1 x 10^{6} to 110 x 10^{6} Pa, interferometry: Waxler RM and Weir 1963
wavelength 589.3 nm, temperature -5 °C to 25 °C, interferometry: Hawkes JB and Astheimer 1948 (see also Hawkes JB and Astheimer 1948)
wavelength 632.8 nm (HeNe laser), temperature 1.03 °C to 59.95 °C; pressure 34.5 x 10^{6} Pa to 1378.8 x 10^{6} Pa, interferometry: Stanley EM 1971a
wavelength 633 nm (HeNe laser); temperature 20 to 35 °C, interferometry: Dobbins HM and Peck 1973
◀ Refractive index of water, complex, real part
■ Refractive index of water, complex, imaginary part, data
■ Refractive index of water, complex, data
■ Refractive index of seawater, complex, real part, data
Refractive index of water, complex, real part, formulas
2 terms: Maron SH et al 1963
see also Eliçabe GE and Garcia-Rubio 1989 (Eq. 9)
3 terms; wavelength 400 to 700 nm; temperature 0 ° to 60 °C; pressure < 110 x 10^{6} Pa: Eisenberg H 1965
3 terms; wavelength 200 to 1100 nm; temperature 25°C; error ≤ 1000 ppm for wavelength 200 to 400 nm, error ≤ 20 ppm for wavelength 400 to 1100: Huibers PDT 1997 (based on the algorithm of Quan Xiaohong and Fry 1995 for seawater)
m' (λ) = 1.31279 + 15.762 λ^{-1} - 4382 λ^{-2} + 1.1455 × 10^{6} λ^{-3} |
where m' is the real part of the refractive index of water and λ is the wavelength of light in vacuum.
4 terms; wavelength 182 nm to 1129 nm, temperature 19°C, 21.5°C, and 24°C: Daimon M and Masumura 2007
4 terms; wavelength DC (static), pressure 10 to 500 MPa, temperature 273, 298, 323, 348 K: Floriano BW and Nascimento 2004 (dielectric function)
6-term Sellmeier formula (three oscillators) wavelength 532 nm to 633 nm, temperature 23 °C, pressure 1 MPa to 250 MPa (or density): Weiss L et al 2012
9 terms; wavelength DC (static), temperature below 0 to 70 °C and pressure 0.1 to 2000 MPa, temperature below 70 to 350 °C and pressure 0.1 to 5000 MPa: Bradley DJ and Pitzer 1979 (dielectric function, see also Weiss L et al 2012, Floriano BW and Nascimento 2004)
10 terms; wavelength 0.2 μm to 1.1 μm; temperature -12 °C to 500 °C; density 0 to 1060 kg m^{-3}, error from ≤ 15 to 1000 ppm: IAPWS 1997. This formula, solved for the real part of the refractive index, m', is reproduced below:
m' = [ ( 1 + 2zρ ) / ( 1 - zρ ) ]^{1/2} | (IAPWS1997) |
where
z = a_{0} + a_{1} ρ + a_{7} ρ^{2} + a_{2} T + a_{3} λ^{2} T + a_{4} / λ^{2} + a_{5} / ( λ^{2} - λ_{UV}^{2} ) + a_{6} / ( λ^{2} - λ_{IR}^{2} ) |
and λ is the wavelength of light in vacuum relative to a wavelength of 589 nm, T is the temperature relative to a temperature of 273.15 K, ρ is density relative to a density of 1000 kg m^{-3}, λ_{UV} = 0.2292020, and λ_{IR} = 5.432937. The coefficients a_{i}, i = 0 to 7, are listed in file RefIndOfWater_IAPWS1997_ai.txt.
This formula is identical with that of Harvey AH et al 1998 who improved the algorithm of Schiebener P et al 1990a, which is based on the algorithm of Thormählen I et al 1985.
Harvey AH et al 1998 provide a set of check values, from which the following sample is taken:
m' = 1.394527 at λ = 226.5 nm, T = 0 °C, p = 0.1 MPa |
m' = 1.320084 at λ = 589.0 nm, T = 100 °C, p = 10 MPa |
m' = 1.324202 at λ = 1013.98 nm, T = 100 °C, p = 100 MPa |
The density of water as a function of temperature and pressure, p, was calculated to 1 ppm by using formulas listed in IAPWS 1996. IAPWS 2009 provides a computationally efficient alternative of comparable accuracy (1 to 30 ppm, about 10 ppm at the atmospheric pressure) to those formulas:
ρ ( T, p ) = [ ( g^{*} / p^{*} ) Σ_{ j = 0 to 7} Σ_{ k = 1 to 6} ( k g_{jk} τ^{ j} π^{ k - 1} ) ]^{-1} |
where ρ is the density [kg m^{-3}], g^{*} = 1 J kg^{-1}, and
τ = ( T - T_{ 0} ) / T^{ *}, T_{ 0} = 273.15 K, T^{ *} = 40 K | |
π = ( p - p_{0} ) / p^{*}, p_{0} = 101325 Pa, p^{*} = 10^{8} Pa |
Note that p_{0} is the standard atmospheric pressure (1 atm). The coefficients g_{jk} are listed in file DensOfWater_IAPWS2009_gjk.txt. IAPWS 2009 provides the following check values:
ρ = (0.100015695)^{-1} × 100 at T = 273.15 K, p = 101325 Pa |
ρ = (0.956683354)^{-1} × 1000 at T = 273.15 K, p = 10^{8} Pa |
ρ = (0.100784471)^{-1} × 100 at T = 313.15 K, p = 101325 Pa |
Burnett JH and Kaplan 2004 point out incorrect representation by Eq. IAPWS1997 of dm' / dT (where T is the temperature) near the 200 nm absorption edge of water (see Fig. 2 in Absorption coefficient of water).
12-term Cauchy-based algorithm; wavelength 226 nm to 1014 nm; temperature 0 to 100 °C: Bashkatov AN and Genina 2002
13 terms; wavelength 400 nm to 700 nm; temperature 0 to 60 °C: Tilton LW and Taylor 1938
◀ Refractive index of water, complex, real part
■ Refractive index of water, complex, models
■ Refractive index of seawater, complex, real part, formulas
Refractive index of water, reviews
Jonasz M and Fournier 2007 (pp. 451-462), Mätzler C et al 2006, Downing HD and Williams 1974, Ray PS 1972, Irvine WM and Pollack 1968
CITATION: Jonasz M. 2007. Refractive index of water (www.mjcopticaltech.com/Publications/RefIndOfWater.php). |
Published: 21-Nov-2007 |
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