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	7004500000000000000♠5.00×10⁴	7003150000000000000♠1.50×10³	1.396	6993110000000000000♠1.1×10⁻⁷	0.069
0.225	7004444000000000000♠4.44×10⁴	7003133000000000000♠1.33×10³	1.373	6992490000000000000♠4.9×10⁻⁸	0.027
0.250	7004400000000000000♠4.00×10⁴	7003120000000000000♠1.20×10³	1.362	6992335000000000000♠3.35×10⁻⁸	0.0168
0.275	7004364000000000000♠3.64×10⁴	7003109000000000000♠1.09×10³	1.354	6992235000000000000♠2.35×10⁻⁸	0.0107
0.300	7004333000000000000♠3.33×10⁴	999	1.349	6992160000000000000♠1.6×10⁻⁸	6997670000000000000♠6.7×10⁻³
0.325	7004308000000000000♠3.08×10⁴	922	1.346	6992108000000000000♠1.08×10⁻⁸	6997418000000000000♠4.18×10⁻³
0.350	7004286000000000000♠2.86×10⁴	857	1.343	6991650000000000000♠6.5×10⁻⁹	6997230000000000000♠2.3×10⁻³
0.375	7004267000000000000♠2.67×10⁴	799	1.341	6991350000000000000♠3.5×10⁻⁹	6997119999999999999♠1.2×10⁻³
0.400	7004250000000000000♠2.50×10⁴	749	1.339	6991186000000000000♠1.86×10⁻⁹	6996584000000000000♠5.84×10⁻⁴
0.425	7004235000000000000♠2.35×10⁴	705	1.338	6991130000000000000♠1.3×10⁻⁹	6996380000000000000♠3.8×10⁻⁴
0.450	7004222000000000000♠2.22×10⁴	666	1.337	6991101999999999999♠1.02×10⁻⁹	6996285000000000000♠2.85×10⁻⁴
0.475	7004211000000000000♠2.11×10⁴	631	1.336	6990935000000000000♠9.35×10⁻¹⁰	6996247000000000000♠2.47×10⁻⁴
0.500	7004200000000000000♠2.00×10⁴	600	1.335	6991100000000000000♠1.00×10⁻⁹	6996250999999999999♠2.51×10⁻⁴
0.525	7004190000000000000♠1.90×10⁴	571	1.334	6991132000000000000♠1.32×10⁻⁹	6996316000000000000♠3.16×10⁻⁴
0.550	7004182000000000000♠1.82×10⁴	545	1.333	6991196000000000000♠1.96×10⁻⁹	6996448000000000000♠4.48×10⁻⁴
0.575	7004174000000000000♠1.74×10⁴	521	1.333	6991360000000000000♠3.60×10⁻⁹	6996787000000000000♠7.87×10⁻⁴
0.600	7004167000000000000♠1.67×10⁴	500	1.332	6992109000000000000♠1.09×10⁻⁸	6997228000000000000♠2.28×10⁻³
0.625	7004160000000000000♠1.60×10⁴	480	1.332	6992138999999999999♠1.39×10⁻⁸	6997279000000000000♠2.79×10⁻³
0.650	7004154000000000000♠1.54×10⁴	461	1.331	6992163999999999999♠1.64×10⁻⁸	6997317000000000000♠3.17×10⁻³
0.675	7004148000000000000♠1.48×10⁴	444	1.331	6992223000000000000♠2.23×10⁻⁸	6997415000000000000♠4.15×10⁻³
0.700	7004143000000000000♠1.43×10⁴	428	1.331	6992335000000000000♠3.35×10⁻⁸	6997601000000000000♠6.01×10⁻³
0.725	7004137999999999999♠1.38×10⁴	414	1.330	6992915000000000000♠9.15×10⁻⁸	0.0159
0.750	7004133000000000000♠1.33×10⁴	400	1.330	6993156000000000000♠1.56×10⁻⁷	0.0261
0.775	7004129000000000000♠1.29×10⁴	387	1.330	6993148000000000000♠1.48×10⁻⁷	0.0240
0.800	7004125000000000000♠1.25×10⁴	375	1.329	6993125000000000000♠1.25×10⁻⁷	0.0196
0.825	7004121000000000000♠1.21×10⁴	363	1.329	6993182000000000000♠1.82×10⁻⁷	0.0282
0.850	7004118000000000000♠1.18×10⁴	353	1.329	6993293000000000000♠2.93×10⁻⁷	0.0433
0.875	7004113999999999999♠1.14×10⁴	343	1.328	6993391000000000000♠3.91×10⁻⁷	0.0562
0.900	7004111000000000000♠1.11×10⁴	333	1.328	6993486000000000000♠4.86×10⁻⁷	0.0679
0.925	7004108000000000000♠1.08×10⁴	324	1.328	6994106000000000000♠1.06×10⁻⁶	0.144
0.950	7004105000000000000♠1.05×10⁴	316	1.327	6994293000000000000♠2.93×10⁻⁶	0.388
0.975	7004103000000000000♠1.03×10⁴	307	1.327	6994348000000000000♠3.48×10⁻⁶	0.449
1.0	7004100000000000000♠1.0×10⁴	300	1.327	6994289000000000000♠2.89×10⁻⁶	0.36
1.2	8300	250	1.324	6994989000000000000♠9.89×10⁻⁶	1.0
1.4	7100	210	1.321	6996138000000000000♠1.38×10⁻⁴	12
1.6	6200	190	1.317	6995855000000000000♠8.55×10⁻⁵	6.7
1.8	5600	170	1.312	6996114999999999999♠1.15×10⁻⁴	8.0
2.0	5000	150	1.306	6997110000000000000♠1.1×10⁻³	69
2.2	4500	136	1.296	6996289000000000000♠2.89×10⁻⁴	17
2.4	4200	125	1.279	6996956000000000000♠9.56×10⁻⁴	50.
2.6	3800	115	1.242	6997317000000000000♠3.17×10⁻³	150
2.65	3770	113	1.219	6995670000000000000♠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]

Notes

↑ 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.
↑ 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

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Optical properties of water and ice

Quantitative description of the refraction index

Refractive Index, Real and Imaginary Parts for Liquid Water

See also

Notes

References