the dependence of the refraction index on the frequency is known through- 

 out the spectrum from V = to V = co and vice versa„ These relations 

 arise from a correlation of these two quantities with the real and imagi- 

 nary parts of a complex dielectric constant, as first noted by Kramers^ . 



The relations are as follows if the dielectric constant k=k + ik^: 



k,(v) - k = - 



1 oo TT 



~°° v'k2(v') 

 V - V 



dv' 



„ r°° k-(v') - k 



kp(v) =r - - V J —2 -5 dv 



'^ ^ v'^ - v^ 



These relations are very general, assuming only the law of cause 

 and effect. Their validity is general and irrespective of the model, 

 which can be either classical or quantum-mechanical. The structural unit 

 can be an atom, electron, molecule, water drop, etc., provided only that 

 a considerable number of them be included in a volume unit whose dimensions 

 are small compared to a wavelength. Qualitatively, the relations state 

 that any change in refractive index is accompanied by absorption of the 

 radiation. 



There are two large regions of the spectrum over which the index 

 of refraction changes appreciably: 1) the region between X-rays and the 

 visible: and 2) that between the visible and the radio- frequency part. 

 In these two regions, therefore, great absorption is to be expected. How- 

 ever, this does not prec 1 ude the existence of windows in these frequency 

 regions. 



The visible region of the spectrum has been discussed above and 

 will be considered below from an experimental viewpoint. Obviously, a 

 window does exist here; the question is how much of one. The region from 

 d. c. to radio-frequency will also be considered below, although at these 

 frequencies the conductivity of water contributes to a large absorption. 

 Ultra-violet and infrared absorption will be considered in the rest of 

 this section. 



In common with other molecules possessing a dipole moment, water 

 molecules exhibit an infrared absorption spectrum. This spectrum arises 

 from the rotational and vibrational degrees of freedom of the molecule; 

 a quantum of radiation induces a transition from one rotational and/or 

 vibrational state to another, being absorbed in the process. The resulting 

 spectrum is quite complicated owing to the fact that water is an asymmetric 

 top molecule, i.e., one that has three different principal moments of inertia. 

 Quantitative formulae for the representation of the rotational energy levels 

 are given in Herzberg's book . The levels for an asymmetric top molecule 



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