34 



STUDIES IN LUMINESCENCE. 



Let P be any point in the slit (Fig. 29). The source of the light reaching 

 P is a cone in the fluorescent liquid converging toward P. The angle of 

 this cone is determined by the aperture of the object glass, EF, of the 

 collimator. Any part of this cone cut off by the glass walls of the cell or 

 by the upper surface of the solution is supplied by total reflection. 



Consider a disk bounded by two circular sections of this cone at distances 

 x and x+dx respectively from the apex P (Fig. 30). The amount of 

 fluorescent light reaching P from such a disk as this will be independent 

 of x, provided no absorption takes place, for, while the area of the section 

 varies as x\ the intensity of the light reaching P from each small portion 

 of the disk varies as 1 .v L> . The fluorescent light that would reach P from 

 such a disk if there were no absorption is therefore kdx, where k is a func- 

 tion of the wave-length, X. 



Fig. 29. 



Fig. 30. 



vSince the light emitted by each section of the cone is in part absorbed, 

 we have for the light reaching P from one of the disks 



di^kdx.e-f* 



and the total lisbt reaching: P from the whole cone is 



= k 

 Jo 



tx dx 



where a is the thickness of the fluorescent solution. 



and k - 

 1- 



Hence 



1 



k. 1 - 



,-fia 



While the i in this expression represents the light reaching one infini- 

 tesimal portion of the slit, it is clear that the total light reaching the slit 

 is proportional to i. It is also evident that k is proportional to the total 

 amount of light, /, of the wave-length considered, that is emitted by the 

 fluorescent substance per unit volume. Hence 



kpl 



J 



,-/3a 



The curve showing the relation between /and X is the "typical fluorescence 

 spectrum." 



To investigate the effect of concentration upon the position of the 

 fluorescence band observations were made in six concentrations. Table 6 

 gives values of observed fluorescence before any correction is made for 

 absorption. Table 8, graphically represented in F A ig. 31, gives the same 

 sets of observations so reduced in scale as to be comparable in intensity 

 with each other. This reduction was made by multiplying the data for 

 each concentration by such a factor as to give wave-length 0.589 /j. the 

 same value as that of the observed fluorescence of the corresponding con- 

 centration in Table 9. 



