# Optical properties of water and ice

The refractive index of water at 20 °C for visible light is 1.33. 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: 

${\frac {n^{2}-1}{n^{2}+2}}(1/{\overline {\rho }})=a_{0}+a_{1}{\overline {\rho }}+a_{2}{\overline {T}}+a_{3}{\overline {\lambda }}^{2}{\overline {T}}+{\frac {a_{4}}{{\overline {\lambda }}^{2}}}+{\frac {a_{5}}{{\overline {\lambda }}^{2}-{\overline {\lambda }}_{\mathit {UV}}^{2}}}+{\frac {a_{6}}{{\overline {\lambda }}^{2}-{\overline {\lambda }}_{\mathit {IR}}^{2}}}+a_{7}{\overline {\rho }}^{2}$ 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)
0.2005.00×1041.50×1031.3961.1×10−70.069
0.2254.44×1041.33×1031.3734.9×10−80.027
0.2504.00×1041.20×1031.3623.35×10−80.0168
0.2753.64×1041.09×1031.3542.35×10−80.0107
0.3003.33×1049991.3491.6×10−86.7×10−3
0.3253.08×1049221.3461.08×10−84.18×10−3
0.3502.86×1048571.3436.5×10−92.3×10−3
0.3752.67×1047991.3413.5×10−91.2×10−3
0.4002.50×1047491.3391.86×10−95.84×10−4
0.4252.35×1047051.3381.3×10−93.8×10−4
0.4502.22×1046661.3371.02×10−92.85×10−4
0.4752.11×1046311.3369.35×10−102.47×10−4
0.5002.00×1046001.3351.00×10−92.51×10−4
0.5251.90×1045711.3341.32×10−93.16×10−4
0.5501.82×1045451.3331.96×10−94.48×10−4
0.5751.74×1045211.3333.60×10−97.87×10−4
0.6001.67×1045001.3321.09×10−82.28×10−3
0.6251.60×1044801.3321.39×10−82.79×10−3
0.6501.54×1044611.3311.64×10−83.17×10−3
0.6751.48×1044441.3312.23×10−84.15×10−3
0.7001.43×1044281.3313.35×10−86.01×10−3
0.7251.38×1044141.3309.15×10−80.0159
0.7501.33×1044001.3301.56×10−70.0261
0.7751.29×1043871.3301.48×10−70.0240
0.8001.25×1043751.3291.25×10−70.0196
0.8251.21×1043631.3291.82×10−70.0282
0.8501.18×1043531.3292.93×10−70.0433
0.8751.14×1043431.3283.91×10−70.0562
0.9001.11×1043331.3284.86×10−70.0679
0.9251.08×1043241.3281.06×10−60.144
0.9501.05×1043161.3272.93×10−60.388
0.9751.03×1043071.3273.48×10−60.449
1.01.0×1043001.3272.89×10−60.36
1.283002501.3249.89×10−61.0
1.471002101.3211.38×10−412
1.662001901.3178.55×10−56.7
1.856001701.3121.15×10−48.0
2.050001501.3061.1×10−369
2.245001361.2962.89×10−417
2.442001251.2799.56×10−450.
2.638001151.2423.17×10−3150
2.6537701131.2196.7×10−5318
2.7037001111.1880.019880
2.7536401091.1570.0592700
2.8035701071.1420.1155160
2.8535101051.1490.1858160
2.9034501031.2010.26811600
2.9533901021.2920.29812700
3.003330100.1.3710.27211400
3.05328098.31.4260.2409990
3.10323096.71.4670.1927780
3.15317095.21.4830.1355390
3.20312093.71.4780.09243630
3.25308092.21.4670.06102360
3.30303090.81.4500.03681400
3.35299089.51.4320.0261979
3.40294088.21.4200.0195721
3.45290086.91.4100.0132481
3.50286085.71.4000.0094340
3.62780831.3850.00515180
3.72700811.3740.00360120
3.82630791.3640.00340110
3.92560771.3570.00380120
4.02500751.3510.00460140
4.12440731.3460.00562170
4.22380711.3420.00688210
4.3233070.1.3380.00845250
4.42270691.3340.0103290
4.52220671.3320.0134370
4.62170651.3300.0147400
4.72130641.3300.0157420
4.82080621.3300.0150390
4.92040611.3280.0137350
5.0200060.1.3250.0124310
5.11960591.3220.0111270
5.21920581.3170.0101240
5.31890571.3120.0098230
5.41850561.3050.0103240
5.51820551.2980.0116380
5.61790541.2890.0142320
5.71750531.2770.0203450
5.81720521.2620.0330710
5.91690511.2480.06221300
6.0167050.1.2650.1072200
6.11640491.3190.1312700
6.2161048.41.3630.08801800
6.3159047.61.3570.05701100
6.4156046.81.3470.0449880
6.5154046.11.3390.0392760
6.6152045.41.3340.0356680
6.7149044.71.3290.0337630
6.8147044.11.3240.0327600
6.9145043.41.3210.0322590
7.0143042.81.3170.0320570

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.