58 SCIENCE PROGRESS 



two points, consistent with their images being recognised 

 separately, is given by the relation — 



d ' = iX/sin a, 



where \ is the wave-length of the light used, in the medium 

 employed, and a is the angle subtended at the point by half 

 the diameter of the object-glass. 



This can be written in the form — 



d = ^X //x sin a 



where \ is the wave-length in air, /j. the refractive index of 

 the medium for this wave-length, and a has the same meaning 

 as before. This form of the expression will be more convenient 

 for our purpose. 



Thus the value of d, the limiting distance, depends on the 

 wave-length of the light used and on the product of ll and 

 sin a, a product which is usually known as the numerical 

 aperture. There are two ways in which d can be diminished 

 and the resolving power of the microscope increased. In the 

 first place, this can be achieved by using a large numerical 

 aperture. If the refractive index /n is given, a is made large : 

 in good objectives this may reach the value 73°, when ll sin a is 

 equal to 0*95 x ll. For air, the numerical aperture would be 

 o - 95, the maximum possible value being unity (when a is 90 ). 

 The value of /i is increased by using objectives of immersion, 

 where the object-glass is immersed in some liquid. If this be 

 water, values of jx sin a up to 1*25 can be obtained. Some- 

 times, especially in mineralogy, a-monobromonaphthalene, 

 which has a refractive index of i'66, is used ; in this case an 

 aperture approaching the value v66 is possible. 



When a liquid of so high a refractive index is used and the 

 lenses are of crown glass, the angle a cannot be increased 

 beyond the angle corresponding to the critical angle for the 

 two substances (67). It is therefore more convenient to use 

 flint glass. 



It follows, from what has been said above, that with such 

 an arrangement we cannot hope to see distinctly objects which 

 are separated by a distance less than about X /3, and this for 

 the sodium lines (\ approximately 6 x io~ 5 cm.) will be 

 2 x io~ G cm. or 0*2 ll} 



1 fi = io~ 4 cm. ; pix = \o~~ cm. 



