78 THE MICROSCOPE. 



Lastly, it should also be noted that it is numerical 

 and not angular aperture which measures the quantity 

 of light admitted to the objective by different pencils. 



First take the case of the medium being the same. 

 The popular notion of a pencil of light may be illus- 

 trated by fig. 43, which assumes that there is equal 

 intensity of emission in all directions, so that the 

 quantity of light contained in any given pencils may 

 be compared by simply comparing the contents of the 

 solid cones. The Bouguer-Lambert law, however, 

 shows that the quantity of light emitted by any 

 bright point varies with the obliquity of the direction 

 of emission, being greater in a perpendicular than in 

 an oblique direction. The rays are less intense in 

 proportion as they are more inclined to the surface 



FIG. 43. FIG. 43a. 



which emits them, so that a pencil is not correctly 

 represented by fig. 43, but by fig. 43, the density of 

 the rays decreasing continuously from the vertical to 

 the horizontal, and the squares of the sines of the 

 semi-angles (i.e., of the numerical aperture) constitut- 

 ing the true measure of the quantity of light con- 

 tained in any solid pencil. 



If, again, the media are of different refractive indices, 

 as air (TO), water (T33), and oil (1'52), the total 

 amount of light emitted over the whole 180 from 

 radiant points in these media under a given illumination 

 is not the same, but is greater in the case of the media 

 of greater refractive indices in the ratio of the squares 

 of those indices (i.e., as TO, 177 and 2'25). The quan- 

 tity of light in pencils of different angle and in different 

 media must therefore be compared by squaring the 



