# Optical properties of water and ice

{{#invoke:main|main}} 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]

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

Where:

and the appropriate constants are ${\displaystyle a_{0}}$ = 0.244257733, ${\displaystyle a_{1}}$ = 0.00974634476, ${\displaystyle a_{2}}$ = −0.00373234996, ${\displaystyle a_{3}}$ = 0.000268678472, ${\displaystyle a_{4}}$ = 0.0015892057, ${\displaystyle a_{5}}$ = 0.00245934259, ${\displaystyle a_{6}}$ = 0.90070492, ${\displaystyle a_{7}}$ = −0.0166626219, ${\displaystyle T^{*}}$ = 273.15 K, ${\displaystyle \rho ^{*}}$ = 1000 kg/m3, ${\displaystyle \lambda ^{*}}$ = 589 nm, ${\displaystyle {\overline {\lambda }}_{\text{IR}}}$ = 5.432937, and ${\displaystyle {\overline {\lambda }}_{\text{UV}}}$ = 0.229202.

In the above expression T is the absolute temperature of water (in K), ${\displaystyle \lambda }$ is the wavelength of light in nm, ${\displaystyle \rho }$ 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 Template:Val Template:Val 1.396 Template:Val 0.069
0.225 Template:Val Template:Val 1.373 Template:Val 0.027
0.250 Template:Val Template:Val 1.362 Template:Val 0.0168
0.275 Template:Val Template:Val 1.354 Template:Val 0.0107
0.300 Template:Val 999 1.349 Template:Val Template:Val
0.325 Template:Val 922 1.346 Template:Val Template:Val
0.350 Template:Val 857 1.343 Template:Val Template:Val
0.375 Template:Val 799 1.341 Template:Val Template:Val
0.400 Template:Val 749 1.339 Template:Val Template:Val
0.425 Template:Val 705 1.338 Template:Val Template:Val
0.450 Template:Val 666 1.337 Template:Val Template:Val
0.475 Template:Val 631 1.336 Template:Val Template:Val
0.500 Template:Val 600 1.335 Template:Val Template:Val
0.525 Template:Val 571 1.334 Template:Val Template:Val
0.550 Template:Val 545 1.333 Template:Val Template:Val
0.575 Template:Val 521 1.333 Template:Val Template:Val
0.600 Template:Val 500 1.332 Template:Val Template:Val
0.625 Template:Val 480 1.332 Template:Val Template:Val
0.650 Template:Val 461 1.331 Template:Val Template:Val
0.675 Template:Val 444 1.331 Template:Val Template:Val
0.700 Template:Val 428 1.331 Template:Val Template:Val
0.725 Template:Val 414 1.330 Template:Val 0.0159
0.750 Template:Val 400 1.330 Template:Val 0.0261
0.775 Template:Val 387 1.330 Template:Val 0.0240
0.800 Template:Val 375 1.329 Template:Val 0.0196
0.825 Template:Val 363 1.329 Template:Val 0.0282
0.850 Template:Val 353 1.329 Template:Val 0.0433
0.875 Template:Val 343 1.328 Template:Val 0.0562
0.900 Template:Val 333 1.328 Template:Val 0.0679
0.925 Template:Val 324 1.328 Template:Val 0.144
0.950 Template:Val 316 1.327 Template:Val 0.388
0.975 Template:Val 307 1.327 Template:Val 0.449
1.0 Template:Val 300 1.327 Template:Val 0.36
1.2 8300 250 1.324 Template:Val 1.0
1.4 7100 210 1.321 Template:Val 12
1.6 6200 190 1.317 Template:Val 6.7
1.8 5600 170 1.312 Template:Val 8.0
2.0 5000 150 1.306 Template:Val 69
2.2 4500 136 1.296 Template:Val 17
2.4 4200 125 1.279 Template:Val 50.
2.6 3800 115 1.242 Template:Val 150
2.65 3770 113 1.219 Template:Val 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]