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TYLER AND PREISENDORFER 



[chap. 8 



value of the slope of this line be designated by a. Then, the relation between 

 Nr and Nq in this range is evidently of the form 



Nr = iVoe-"''. 



(10) 



ln(A/^/A/Q 



Range of linearity 

 Fig. 4. Semi-log plot of radiance ratio against the path length through water. 



This is the well-known experimentally based equation for the attenuation of a 

 beam of light. The value of a obtained is independent of Nq and is valid only 

 if Nr represents flux that has come directly from the source and if the distance, 

 r, is chosen so as to be within the region of linearity. 



dNr = - ocNr dr. 



(11) 



Fig. 5. Schematic drawing of experiment to detect radiation outside the limits of the 

 direct beam. 



From the differential statement of equation (10), given in equation (11), we 

 conclude that a is an inherent property of the medium which gives the attenua- 

 tion per unit length of a beam of light passing through the medium. Returning 

 to the original experimental setup, careful measurements Jws^ outside the beam 

 (Fig. 5) will reveal radiation that can be positively identified as coming from 

 the beam. From this we conclude that the attenuation of the beam's radiance 

 is partially due to a redirection or scattering of some of its flux out of the main 

 direction of travel of the beam. A critical examination of the scattered flux 



