NUMERICAL APERTURE. 165 



as lo inches, and the magnifying power of this lens is supposed 



to be 80, that is to say, 



10 ,' I • 1 



^- = 80 or /= ^ inch. 



/ ^ 



This number, 80, multipHed by an ocular magnifying 



5 times (A ocular) gives the magnifying power 400, and this holds 



good for all the other powers. 



The rule for the magnifying power of an objective is, divide 10 

 by the focal length in inches, and multiply the quotient by the 

 power of the eyepiece. 



In the case of minute objects, some of which are transparent 

 and some opaque, the waves of light pass round them, or through 

 them, or both together, and thus may cause a disturbance in their 

 undulations. In this case images known as Diffraction Images are 

 formed. 



In viewing minute objects it is important to combine as many 

 as possible of these images ; but these images are dispersed at 

 various angles from the perpendicular to the surface, and in a 

 denser medium than air these angles are of course reduced 

 according to the index of refraction, whicli proportion is given in 

 the formula for numerical aperture. An immersion lens therefore can 

 take more of these images in, and thus has greater resolving power. 



Take, for instance, a lens of 170'' angular aperture; this, if a 

 dry lens, has a numerical aperture of o"9962, but if oil immersion 

 of I "5 14224, or the oil lens has more than half as much again 

 resolving power as the dry lens, though the dry lens is working 

 almost at its maximum. This could never have been inferred 

 from the angular aperture alone. 



If the wave-length of green light is taken as inch (this 



50,000 



is a point between E and F in the spectrum) the numerical aper- 

 ture, multiplied by 100,000, will give a theoretical resolving power 

 in lines to the inch, which is often very convenient, though of 

 course rather rough. 



For example : required a lense to resolve Amphipleura Pellurida, 

 which contains about 90,000 lines to the inch. To 90,000 add a 

 tenth for errors, etc. ; this makes 99,000; divide by 100,000. This 

 gives N A = -99 ^ sin 82° for a dry lens, = m sin a = 48° for 



