444 Table 155 



REFLECTIVITY OF A WATER SURFACE 



The reflectivity of a plane water surface for unpolarized light is a function of the angle 

 of incidence of the light and the index of refraction of the water and may be computed 

 from the reflection law of Fresnel 



1 [sin 8 (i — r) , tan" (i — r)~\ 



R J_ [" sin" (i — r) 

 2 Lsin'O' + r)" 1 " 



(i + r) tan a (i + r)J 

 where 



R ^reflectivity, 

 t'=angle of incidence, 

 r= angle of refraction, 



i and r are related to the index of refraction n of the water by n = sin j'/sin r. Although 

 the values given are valid only for a plane undisturbed water surface, Angstrom * states : 

 ". . . . it is evident that the observed reflection from disturbed water-surfaces only shows 

 small deviations from the values which are to be expected from the Fresnel formula. 

 .... Some investigations which I have carried out on artificially disturbed surfaces 

 seem to indicate that the deviation from the Fresnel formula is positive for slight dis- 

 turbances of the surface, but negative when the amplitude gets large compared with the 

 wave-length of the water waves. The measurements give strong support to the view that 

 in the average case in geophysical discussions we may base computations of the reflection, 

 absorption, and emission power of water-surfaces on the validity of the Fresnel formula." 



Values in Table 155 are computed on the assumption that n = 1.333, the value of the 

 index of refraction for pure water. The value for sea water is slightly larger, about 

 1.3398 for sea water of salinity 35%c, but the difference is negligible. 



In considering direct solar radiation, the angle of incidence i = sun's zenith distance. 



i 0° 10° 20° 30° 40° 50° 60° 70° 80° 85° 90° 



R{%) 2.0 2.0 2.1 2.1 2.5 3.4 6.0 13.4 34.8 58.4 100.0 



'Angstrom, A., Geograf. Ann., vol. 7, p. 323, 1925. 



SMITHSONIAN METEOROLOGICAL TABLES 



