UNEQUAL INT HNS IT V OF KMITTKI) LIMIT 



of light alone more light can always be obtained in the image by 

 t li i-o \vin_i: more upon the object but no increase in the amount of illu- 

 mination ran make a <hy lens equal in per formance a s re^an Is aperture 

 to a wide-angled immersion lens. 



The popular notion of a pencil of light may be illustrated by 

 fig. 33, which assumes that there is equal intensity of emission in 

 all directions, and that the intensity of a portion of the pencil taken 

 close to the perpendicular is identical with that of another portion 

 of equal angular extension, but morp removed from the perpendicular. 

 On this view, therefore, the quantity of light contained in any given 

 pencils may be compared by simply comparing the contents of the 

 >olid cones. 



When, however, aperture is considered, and the values of n sin u 

 are worked out for particular cases, they are seen to differ from 



FIG. 33. Diagram showing erroneous inference as to the intensity of emitted rays. 



those obtained by estimating in the above manner the amount of 

 light in the solid cones, and some perplexity naturally arises from 

 the supposition that the measure of the aperture of the objective does 

 not correspond to that of the quantity of light which it admits. 



All this arises from the mistaken assumption that a luminous 

 pencil is properly represented by fig. 33. 



In the last century (1760) Bouguet 1 and Lambert 2 established 

 the important fact that 

 with any -urtace of uni- 

 form I'ti'I'nif.ioii the inten- 

 sity of the emitted rays is 

 not the same in all direc- 

 tions. The {tower of emis 

 sion and the intensity of 

 the rays (i.e. the quantity 

 of li;lit emanating from 

 a given surface-element 

 within a cone of given 

 narrow angle) varies in 



the proportion of the co- ,- 



1 ... /.IT FIG. 34. The intensity of emitted rays is not the 



sine ot the angle of obliqui- same m a n directions. 



ty under which the ray is 



emitted ; iii other words, in the proportion of the cosine, of the angle 



of deflection from the perpendicular to the luminous surface under 



Traitt d'Optique sur la Gradation de la Luinii-re, 1760. 

 -' ' 1760. 



E2 



