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).

To various degrees, all transparent media are dispersive, which means that the amount by which they bend light varies with its wave length. Specifically, in the visible portion of the spectrum (approximately 4300-6900 Angstroms) the index of refraction is generally a decreasing function of wave length: violet light is bent more than red light. Furthermore, the rate of change of the index of refraction also increases as the wave length decreases. And, the index of refraction usually increases with the density of the medium. Water displays all of these characteristics. Table 1 shows the results of some measurements (Tilton and Taylor) of the index of refraction of water, n(w), with respect to dry air having the same temperature T as the water and at a pressure of 760 mm-Hg.

          
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.

Sea water contains dissolved impurities, primarily in the form of dissociated salts of sodium, magnesium, calcium, and potassium. Its density, and hence n(w), therefore depends on its salinity, a quantity usually expressed as grams of salts dissolved in a kilogram of sea water (gm/kg), or parts per thousand by weight. Table 2 (taken from Dorsey) shows how n(w) increases with salinity for the sodium D-lines (mean:5893 Angstroms) at 18 degrees C.

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.