# Optical properties of water and ice

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

The real part of the index of refraction is described by the following 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:

 $a_0=0.244257733$ $a_1=0.00974634476$ $a_2=-0.00373234996$ $a_3=0.000268678472$ $a_4=0.0015892057$ $a_5=0.00245934259$ $a_6=0.90070492$ $a_7=-0.0166626219$ $\overline T = \frac{T}{T^{\text{*}}}$ $\overline \rho = \frac{\rho}{\rho^{\text{*}}}$ $\overline \lambda = \frac{\lambda}{\lambda^{\text{*}}}$ $T^{\text{*}}= 273.15$ K $\rho^{\text{*}}= 1000$ kg/m3 $\lambda^{\text{*}} = 589$ nm $\overline\lambda_{\text{IR}}=5.432937$ $\overline\lambda_{\text{UV}}=0.229202$

And T is the absolute temperature of water (in K), $\lambda$ is the wavelength, $\rho$ is the density of the water and n is the index of refraction.

## Notes

1. ^ 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.

## 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