# Index of Refraction of Water

The index of refraction of a transparent medium is a measure of its ability to alter the direction of propagation of a ray of light entering it. If light were to travel through empty space and then penetrate a planar water surface, the measured angles of incidence and refraction could be substituted into Snell's Law (see "Refraction of Light by Water") to yield the index of refraction of water "relative to vacuum". The only variables would be those associated with the physical state of the water. But, in practice, it is simpler to conduct experiments using an air/water interface to obtain the index of refraction of water relative to air, and then to convert it from air to vacuum by applying appropriate corrections. The result, which is always greater than one, is the ratio of the phase velocity of light in a vacuum to its phase velocity in water: light travels more slowly in water than in a vacuum (or in air).

```
Table 1: Index of refraction of water as a
function of wave length and water temperature.
----------------------------------------------
Wave Length
(Angstroms)   T=10 C   T=20 C   T=30 C

7065      1.3307   1.3300   1.3290
5893      1.3337   1.3330   1.3319
5016      1.3371   1.3364   1.3353
4047      1.3435   1.3427   1.3417

```

To convert the tabulated values to indices relative to vacuum, add 4 to the fourth decimal place. Note that n(w) increases as the temperature of the water decreases. This is consistent with our expectations, since the density of water increases as it cools. It is interesting, however, that if the measurements are extended to lower temperatures the index does not show an anomaly at 4 degrees C, in spite of the fact that the water density peaks at that temperature.

```Table 2. Changes in index of refraction due to salinity
--------------------------------------------------------
salinity
(gm/kg)     increase in n(w)          example
--------------------------------------------------------
5            0.00097           northern Baltic Sea
10            0.00194
15            0.00290
20            0.00386           bight of Biafra
25            0.00482
30            0.00577
35            0.00673           Atlantic surface
40            0.00769           northern Red Sea
```

The index of refraction is also a function of water pressure, but the dependence is quite weak because of the relative incompressibility of water. In fact, over the normal ranges of temperatures (0-30 C), the approximate increase in n(w) is 0.000016 when the water pressure increases by one atmosphere.

Clearly, the most significant factors affecting n(w) are the wave length of the light and the salinity of the water. Even so, n(w) varies by less than 1% over the indicated range of values of these variables. For most practical purposes it is sufficient to adopt the value n(w)=4/3.

REFERENCES:

L. W. Tilton and J. K. Taylor, J. Res. Nat. Bur. Stand., 20, 419 (RP1085) 1938.

E. Dorsey, "Properties of Ordinary Water-Substance", (Reinhold Publishing Corporation 1940).