Optical properties of water and ice

Main article: Properties of water

The refractive index of water at 20°C is 1.332986. The refractive index of normal ice is 1.31. (From List of refractive indices.) In general, an index of refraction is a complex number with both a real and imaginary part, where the latter indicates the strength of absorption loss at a particular wavelength. In the visible part of electromagnetic spectrum the imaginary part of the refractive index is very small. However, water and ice absorb in infrared and close the atmospheric window thereby contributing to the greenhouse effect

The absorption spectrum of pure water is used in numerous applications, including light scattering and absorption by ice crystals and cloud water droplets, theories of the rainbow, determination of the single scattering albedo, ocean color, and many others.

Quantitative description of the refraction index

Over the wavelengths from 0.2 μm to 1.2 μm, and over temperatures from −12°C to 500°C the real part of the index of refraction of water can be calculated by the following empirical expression: [1]

\frac{n^{2}-1}{n^{2}+2}(1/\overline{\rho })=a_{0}+a_{1}\overline{\rho}+a_{2}\overline{T}+a_{3}{\overline{\lambda}}^{2}\overline{T}+\frac{a_{4}}{{\overline{\lambda}}^{2}}+\frac{a_{5}}{{\overline{\lambda }}^{2}-{\overline{\lambda}}_{\mathit{UV}}^{2}}+\frac{a_{6}}{{\overline{\lambda}}^{2}-{\overline{\lambda }}_{\mathit{IR}}^{2}}+a_{7}{\overline{\rho}}^{2}

Where:

\overline T = \frac{T}{T^{\text{*}}}, \text{ }
\overline \rho = \frac{\rho}{\rho^{\text{*}}}, \text{ and }
\overline \lambda = \frac{\lambda}{\lambda^{\text{*}}}

and the appropriate constants are a_0 = 0.244257733, a_1 = 0.00974634476, a_2 = −0.00373234996, a_3 = 0.000268678472, a_4 = 0.0015892057, a_5 = 0.00245934259, a_6 = 0.90070492, a_7 = −0.0166626219, T^{*} = 273.15 K, \rho^{*} = 1000 kg/m3, \lambda^{*} = 589 nm, \overline\lambda_{\text{IR}} = 5.432937, and \overline\lambda_{\text{UV}} = 0.229202.

In the above expression T is the absolute temperature of water (in K), \lambda is the wavelength of light in nm, \rho is the density of the water in kg/m3, and n is the real part of the index of refraction of water.

Refractive Index, Real and Imaginary Parts for Liquid Water

Refractive Index of Liquid Water
Wavelength (μm) Wavenumber (cm−1) Frequency (THz) n k α' (cm−1)
0.200 5.00×104 1.50×103 1.396 1.1×10−7 0.069
0.225 4.44×104 1.33×103 1.373 4.9×10−8 0.027
0.250 4.00×104 1.20×103 1.362 3.35×10−8 0.0168
0.275 3.64×104 1.09×103 1.354 2.35×10−8 0.0107
0.300 3.33×104 999 1.349 1.6×10−8 6.7×10−3
0.325 3.08×104 922 1.346 1.08×10−8 4.18×10−3
0.350 2.86×104 857 1.343 6.5×10−9 2.3×10−3
0.375 2.67×104 799 1.341 3.5×10−9 1.2×10−3
0.400 2.50×104 749 1.339 1.86×10−9 5.84×10−4
0.425 2.35×104 705 1.338 1.3×10−9 3.8×10−4
0.450 2.22×104 666 1.337 1.02×10−9 2.85×10−4
0.475 2.11×104 631 1.336 9.35×10−10 2.47×10−4
0.500 2.00×104 600 1.335 1.00×10−9 2.51×10−4
0.525 1.90×104 571 1.334 1.32×10−9 3.16×10−4
0.550 1.82×104 545 1.333 1.96×10−9 4.48×10−4
0.575 1.74×104 521 1.333 3.60×10−9 7.87×10−4
0.600 1.67×104 500 1.332 1.09×10−8 2.28×10−3
0.625 1.60×104 480 1.332 1.39×10−8 2.79×10−3
0.650 1.54×104 461 1.331 1.64×10−8 3.17×10−3
0.675 1.48×104 444 1.331 2.23×10−8 4.15×10−3
0.700 1.43×104 428 1.331 3.35×10−8 6.01×10−3
0.725 1.38×104 414 1.330 9.15×10−8 0.0159
0.750 1.33×104 400 1.330 1.56×10−7 0.0261
0.775 1.29×104 387 1.330 1.48×10−7 0.0240
0.800 1.25×104 375 1.329 1.25×10−7 0.0196
0.825 1.21×104 363 1.329 1.82×10−7 0.0282
0.850 1.18×104 353 1.329 2.93×10−7 0.0433
0.875 1.14×104 343 1.328 3.91×10−7 0.0562
0.900 1.11×104 333 1.328 4.86×10−7 0.0679
0.925 1.08×104 324 1.328 1.06×10−6 0.144
0.950 1.05×104 316 1.327 2.93×10−6 0.388
0.975 1.03×104 307 1.327 3.48×10−6 0.449
1.0 1.0×104 300 1.327 2.89×10−6 0.36
1.2 8300 250 1.324 9.89×10−6 1.0
1.4 7100 210 1.321 1.38×10−4 12
1.6 6200 190 1.317 8.55×10−5 6.7
1.8 5600 170 1.312 1.15×10−4 8.0
2.0 5000 150 1.306 1.1×10−3 69
2.2 4500 136 1.296 2.89×10−4 17
2.4 4200 125 1.279 9.56×10−4 50.
2.6 3800 115 1.242 3.17×10−3 150
2.65 3770 113 1.219 6.7×10−5 318
2.70 3700 111 1.188 0.019 880
2.75 3640 109 1.157 0.059 2700
2.80 3570 107 1.142 0.115 5160
2.85 3510 105 1.149 0.185 8160
2.90 3450 103 1.201 0.268 11600
2.95 3390 102 1.292 0.298 12700
3.00 3330 100. 1.371 0.272 11400
3.05 3280 98.3 1.426 0.240 9990
3.10 3230 96.7 1.467 0.192 7780
3.15 3170 95.2 1.483 0.135 5390
3.20 3120 93.7 1.478 0.0924 3630
3.25 3080 92.2 1.467 0.0610 2360
3.30 3030 90.8 1.450 0.0368 1400
3.35 2990 89.5 1.432 0.0261 979
3.40 2940 88.2 1.420 0.0195 721
3.45 2900 86.9 1.410 0.0132 481
3.50 2860 85.7 1.400 0.0094 340
3.6 2780 83 1.385 0.00515 180
3.7 2700 81 1.374 0.00360 120
3.8 2630 79 1.364 0.00340 110
3.9 2560 77 1.357 0.00380 120
4.0 2500 75 1.351 0.00460 140
4.1 2440 73 1.346 0.00562 170
4.2 2380 71 1.342 0.00688 210
4.3 2330 70. 1.338 0.00845 250
4.4 2270 69 1.334 0.0103 290
4.5 2220 67 1.332 0.0134 370
4.6 2170 65 1.330 0.0147 400
4.7 2130 64 1.330 0.0157 420
4.8 2080 62 1.330 0.0150 390
4.9 2040 61 1.328 0.0137 350
5.0 2000 60. 1.325 0.0124 310
5.1 1960 59 1.322 0.0111 270
5.2 1920 58 1.317 0.0101 240
5.3 1890 57 1.312 0.0098 230
5.4 1850 56 1.305 0.0103 240
5.5 1820 55 1.298 0.0116 380
5.6 1790 54 1.289 0.0142 320
5.7 1750 53 1.277 0.0203 450
5.8 1720 52 1.262 0.0330 710
5.9 1690 51 1.248 0.0622 1300
6.0 1670 50. 1.265 0.107 2200
6.1 1640 49 1.319 0.131 2700
6.2 1610 48.4 1.363 0.0880 1800
6.3 1590 47.6 1.357 0.0570 1100
6.4 1560 46.8 1.347 0.0449 880
6.5 1540 46.1 1.339 0.0392 760
6.6 1520 45.4 1.334 0.0356 680
6.7 1490 44.7 1.329 0.0337 630
6.8 1470 44.1 1.324 0.0327 600
6.9 1450 43.4 1.321 0.0322 590
7.0 1430 42.8 1.317 0.0320 570

The total refractive index of water is given as m = n + ik. The absorption coefficient α' is used in the Beer–Lambert law with the prime here signifying base e convention. Values are for water at 25°C, and were obtained through various sources in the cited literature review.[2]

See also

Notes

  1. ↑ The International Association for the Properties of Water and Steam (1997). "Release on the Refractive Index of Ordinary Water Substance as a Function of Wavelength, Temperature and Pressure" (PDF). Retrieved 2008-10-08.
  2. ↑ Hale, George; Querry, Marvin (1 March 1973). "Optical Constants of Water in the 200-nm to 200μm Wavelength Region". Applied Optics (Optical Society of America) 12 (3): 555–563. doi:10.1364/AO.12.000555. Retrieved 8 January 2014.

References

  • R. M. Pope and E. S. Fry, Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements, Appl. Opt., 36, 8710-8723, 1997.
  • Mobley, Curtis D., Light and water : radiative transfer in natural waters; based in part on collaborations with Rudolph W. Preisendorfer, San Diego, Academic Press, 1994, 592 p., ISBN 0-12-502750-8