# Refractive index of water

Most people would assume that the refractive index of water is known to a high degree of accuracy.  However, as shown in Fig. 1, the published literature reveals significant differences in the values of refractive index of water for a given wavelength.

 Fig. 1  Refractive index of water as a function of wavelength

The data sources used in Fig. 1 are:

Each value of refractive index corresponds to a "rainbow angle" derived from geometric optics: the computed values for the primary rainbow are shown in Fig 2, whilst those for the secondary rainbow are shown in Fig 3.

 Fig. 2  Primary rainbow angle as a function of wavelength Fig. 3  Secondary rainbow angle as a function of wavelength

The lack of agreement between the values of refractive index shown in Fig. 1 is important because Figs. 2 and 3 indicate differences in rainbow angles of more than 0.5° for the primary rainbow and of almost 2° for the secondary rainbow.  By default, the MiePlot program uses the IAPWS calculation method for water at a temperature of 5° C.  As the IAPWS values of refractive index of water varies slightly with temperature (as shown in Fig. 4 below), MiePlot allows users to specify other temperatures.

 Fig. 4   Variation of IAPWS refractive index of water with temperature

The refractive index of any substance is best described as a complex number, such as 1.34 + i 0.00067.  The real part of this number is the "ordinary" refractive index as discussed above, whilst the imaginary part indicates the amount of absorption.  If the imaginary part is zero, the substance is non-absorbing.  For most practical purposes, the complex part of the refractive index of water can be ignored in the visible spectrum (e.g. 400 - 700 nm), but Fig. 5 shows two estimates of its value.

 Fig. 5   Imaginary part of the refractive index of water

Fig. 5 has been derived from two independent sources:

• R.M. Pope and E.S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements", Applied Optics, 36, 33, pp. 8710 - 8723 (20 Nov. 1997)
• D. Segelstein, "The Complex Refractive Index of Water", M.S. Thesis, University of Missouri, Kansas City (1981). A summary of the refractive index data can be downloaded from here or it is included as "Segelstein.txt" when downloading the MiePlot program.
Note that the Pope & Fry specify the absorption coefficient (aw) rather than the imaginary part of the refractive index.  The two quantities are related by the following formula:

Imaginary part = λ * 1E-9 * aw /(4 * π)
(where λ is the wavelength measured in nm and aw is measured per metre)

For example, Pope & Fry specify an absorption coefficient per metre of aw = 0.34 at wavelength λ = 650 nm, corresponding to an imaginary part of the refractive index = 1.75866E-8 .

The following table shows numerical values for the refractive index of water as a function of wavelength in the visible part of the spectrum, together with the approximate colour (the colour has been calculated according to the method shown on the previous page).  Note that the real part of the refractive index has been calculated using the IAPWS method for 5 C, whereas the imaginary part has been interpolated from Pope & Fry' s data.

 Wavelength (nm) Refractive index Colour Real part Imaginary part 400 1.34451 2.11E-10 425 1.34235 1.62E-10 450 1.34055 3.30E-10 475 1.33903 4.31E-10 500 1.33772 8.12E-10 525 1.33659 1.74E-09 550 1.33560 2.47E-09 575 1.33472 3.53E-09 600 1.33393 1.06E-08 625 1.33322 1.41E-08 650 1.33257 1.76E-08 675 1.33197 2.41E-08 700 1.33141 3.48E-08
 Fig. 6   Segelstein's values for the complex refractive index of water for wavelengths from 10 nm to 10m

Fig. 6 shows Segelstein's values for the complex refractive index of water for wavelengths between 10 nm and 10 m.  Although the imaginary part of the refractive index can generally be ignored in the visible spectrum (e.g. 400 - 700 nm), Fig. 6 emphasises that this approximation is not valid at ultra-violet and infra-red wavelengths.

Fig. 7 Segelstein's values for the real part of the refractive index of water for
wavelengths from 10 nm to 10m

Fig. 7 is an expanded version of Fig. 6 showing only the real part of the refractive index given by Segelstein (using a linear scale for the vertical axis).

Although the IAPWS formulation is probably the most accurate, it has two disadvantages:
• it provides only the real part of the refractive index of water;
• it is valid only for a limited range of wavelengths - the IAPWS documentation states that it is valid for the range 0.2 - 1.1 μm (200 - 1100 nm) but adds that it "is in good agreement with recent results in liquid water at wavelengths up to 1.9 μm" (1900 nm).
Segelstein's values address both of these issues but, as shown in Fig. 8 below, there are substantial differences in the real part of the refractive index of water compared with the IAPWS results. These differences are significant, whereas the differences in the imaginary part of the refractives index shown in Fig. 6 can be safely ignored for most purposes.

Fig. 8 Comparison of Segelstein's values with those of IAPWS

The MiePlot program offers the option of using real or complex values of refractive index.  When using the IAPWS values for the real part of the refractive index, MiePlot uses the Segelstein data for the imaginary part in the visible spectrum.  As Segelstein's data for real and imaginary values of refractive index of water cover a much wider range of wavelengths, it is invaluable for use beyond the visible spectrum. However, Figs. 1 - 3 indicate the need for caution when using Segelstein's values of real refractive index within the visible spectrum.

Comprehensive information about refractive index data for many other substances is available at RefractiveIndex.info.

Page updated on 7 December 2016