:Optical properties of water and ice

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:{{cite report

| author = The International Association for the Properties of Water and Steam

| title = Release on the Refractive Index of Ordinary Water Substance as a Function of Wavelength, Temperature, and Pressure (IAPWS R9-97)

| date= September 1997

| url= http://www.iapws.org/relguide/rindex.pdf

| accessdate = 2008-10-08}}

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

Where:

:$\backslash overline\; T\; =\; \backslash frac\{T\}\{T^\{\backslash text\{*\}\}\}$,

:$\backslash overline\; \backslash rho\; =\; \backslash frac\{\backslash rho\}\{\backslash rho^\{\backslash text\{*\}\}\}$, and

:$\backslash overline\; \backslash lambda\; =\; \backslash frac\{\backslash lambda\}\{\backslash lambda^\{\backslash text\{*\}\}\}$

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,$\backslash rho^\{*\}$ = 1000 kg/m³, $\backslash lambda^\{*\}$ = 589 nm, $\backslash overline\backslash lambda\_\{\backslash text\{IR\}\}$ = 5.432937, and $\backslash overline\backslash lambda\_\{\backslash text\{UV\}\}$ = 0.229202.

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

In the above formula, the density of water also varies with temperature and is defined by:{{Cite web|url=https://metgen.pagesperso-orange.fr/metrologiefr19.htm|title=Calcul de la masse volumique de l'EAU}}{{Cite web|url=https://www.econology.info/masse-volumique-eau-temperature/|title = Density of water and temperature - Physical Sciences, Chemistry and Biology|date = 10 February 2009}}

$\backslash rho(t)\; =\; a\_5\; \backslash left(\; 1-\backslash frac\{(t+a\_1)^2(t+a\_2)\}\{a\_3(t+a\_4)\}\; \backslash right)$

with:

• $a\_1$ = −3.983035 °C
• $a\_2$ = 301.797 °C
• $a\_3$ = 522528.9 °C²
• $a\_4$ = 69.34881 °C
• $a\_5$ = 999.974950 kg / m³

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.{{cite journal |last1=Hale |first1=George |last2=Querry |first2=Marvin |date=1 March 1973 |title=Optical Constants of Water in the 200-nm to 200μm Wavelength Region |url=https://www.osapublishing.org/ao/fulltext.cfm?uri=ao-12-3-555 |journal=Applied Optics |publisher=Optical Society of America |volume=12 |issue=3 |pages=555–563 |doi=10.1364/AO.12.000555 |pmid=20125343 |accessdate=8 January 2014|bibcode=1973ApOpt..12..555H|url-access=subscription }}

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

{{Reflist}}

{{refbegin}}

• 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}}

{{refend}}

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