PRINCIPLES OF STEREOSCOPIC VISION 89 



image-distance. For example, a moderately short-sighted eye sees 

 distinctly at 150 mm. as its .shortest distance, and at 300 mm. as 

 its longest distance; then the numerical equivalent of the extent 

 of accommodation would be equal to ^-J-jj mm.; the calculation for 

 an object in air would give a depth of vision by accommodation 



amounting to 



2-08 rum. with 10 times amplification 



0-23 30 



0-02 100 



0-0023 ,. 300 



0-00021 ,. 1000 



0-00002 ,, 3000 



These figures are modified by the medium in which the object is 

 placed and by the greater or less shortness and length of vision. 



Secondly, the perception of depth is assisted by the insensi- 

 bility of the eye to small defects in the union of the rays in the optic 

 image, and therefore to small circles of confusion in the visual image. 

 Trans\erse sections of the object which are a little above and below 

 the exact focal adjustment are seen without prejudicial effects. The 

 total effect so ol>i'i nl is the so-called pf net rut ion or <l>'j>tlt of f<-,i>. 

 of an objective. This may be determined numerically by defining 

 the allowable magnitude of the circles of confusion in the micro- 

 scopical image by the visual angle under which they appear to the eye. 

 Tt is found that one minute of arc denotes the limit of sharply 

 defined vision, two to three minutes for fairly distinct vision, and live 

 to six minutes the limits of vision only just tolerable. This being 

 determined, the focal depth depends only on the refractive index of 

 the medium in which the object is placed, the amplification, and the 

 angle of aperture, and it is directly proportional to the refractive 

 index of the object medium, and inversely proportional to the 

 ' numerical aperture ' of the objective, as also to the first power of 

 the amplification. These assume the visible angle of allowable 

 indistinctness to be fixed at 5', the aperture angle of the image- 

 forming pencils to be 60 in air ; the depth of focus of an object in 

 ail' will then be 



0-073 mm. for 10 times amplification 

 0-024 30 



0-0073 

 0-0024 

 0-00073 

 0-00024 



100 



300 



1000 



3000 



l>y limiting or enlarging the allowable magnitude of indistinctness 

 in the image we correspondingly modify these figures, as we should 

 do with media of different refractive indices and increased aperture- 



angle. 



It is plain, then, that the actual depth of vision must always be 

 the exact sum of the accommodation depth and focal depth. The 

 former expresses the object space through which the eye by the play 

 of accommodation can penetrate and secure a sharp image ; the latter 

 gives the amount by which this object-space is extended in its 

 limits reckoning both from above and below because without per- 

 fect sharpness of image there is still a sufficient distinctness of vision. 



