Optical properties of water and ice

Short description: none

Absorption of light in water

The refractive index of water at 20 °C for visible light is 1.33.[1] 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 real and imaginary parts, where the latter indicates the strength of absorption loss at a particular wavelength. In the visible part of the electromagnetic spectrum, the imaginary part of the refractive index is very small. However, water and ice absorb in infrared and close the infrared 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.

## Contents

* 1 Quantitative description of the refraction index
* 2 Volumic mass of water
* 3 Refractive index (real and imaginary parts) for liquid water
* 4 See also
* 5 Notes
* 6 References

## Quantitative description of the refraction index

Over the wavelengths from 0.2 to 1.2 μm, and over temperatures from −12 to 500 °C (261 to 773 K), the real part of the index of refraction of water can be calculated from the following empirical expression:[2] n2−1n2+21ρ¯=a0+a1ρ¯+a2T¯+a3λ¯2T¯+a4λ¯2+a5λ¯2−λ¯UV2+a6λ¯2−λ¯IR2+a7ρ¯2, where T¯=T/T*, ρ¯=ρ/ρ*, λ¯=λ/λ*, and the constants are

a0 = 0.244257733,
a1 = 0.00974634476,
a2 = −0.00373234996,
a3 = 0.000268678472,
a4 = 0.0015892057,
a5 = 0.00245934259,
a6 = 0.90070492,
a7 = −0.0166626219,

T* = 273.15 K,
ρ* = 1000 kg/m3,
λ* = 0.589 μm,
λ¯IR = 5.432937 μm,
λ¯UV = 0.229202 μm.

In the above expression, T is the absolute temperature of water, λ is the wavelength of light, ρ is the density of the water, and n is the real part of the index of refraction of water.

## Volumic mass of water

In the above formula, the density of water also varies with temperature and is described by[3][4] ρ(t)=a5(1−(t+a1)2(t+a2)a3(t+a4)) with t in °C and

a1 = −3.983035 °C,
a2 = 301.797 °C,
a3 = 522528.9 °C2,
a4 = 69.34881 °C,
a5 = 999.974950 kg/m3.

## 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.[5]

## See also

* Absorption (electromagnetic radiation)
* Atmospheric radiative transfer codes
* Color of water
* Electromagnetic absorption by water
* Ocean color
* Ocean optics
* List of refractive indices

## Notes

1. ↑ Lide, David R. (2003-06-19) (in en). CRC Handbook of Chemistry and Physics, 84th Edition. CRC Handbook. CRC Press. 8—Concentrative Properties of Aqueous Solutions: Density, Refractive Index, Freezing Point Depression, and Viscosity. ISBN 9780849304842. https://books.google.com/books?id=kTnxSi2B2FcC.
2. ↑ The International Association for the Properties of Water and Steam (September 1997). ﻿Release on the Refractive Index of Ordinary Water Substance as a Function of Wavelength, Temperature, and Pressure (IAPWS R9-97)﻿ (Report). http://www.iapws.org/relguide/rindex.pdf. Retrieved 2008-10-08.
3. ↑ "Calcul de la masse volumique de l'EAU". https://metgen.pagesperso-orange.fr/metrologiefr19.htm.
4. ↑ "Density of water and temperature". 10 February 2009. https://www.econology.info/masse-volumique-eau-temperature/.
5. ↑ 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. PMID 20125343. Bibcode: 1973ApOpt..12..555H. https://www.osapublishing.org/ao/fulltext.cfm?uri=ao-12-3-555. 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

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Optical properties of water and ice. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Optical_properties_of_water_and_ice&oldid=4335775"