38 METHODS OF PETR<><;U.\I>HK MICROSCOPIC RESEARCH. 
surrounding the objective. The higher the refractive index, the higher the 
numerical aperture of the objective for the same apertural angle of the inci- 
dent rays. In case the objective be a dry objective (object space is air and 
consequently n = i ), the numerical aperture is directly the sine of the angle 
included by the incident cone of rays. Its highest possible value is accor- 
dingly i. In case the objective be immersed in oil, correspondingly higher 
numerical apertures are obtainable and at the same time better spherical 
corrections, because of the advantage taken of the aplanatic points of the 
front lens in the construction of such systems. 
The importance of the numerical aperture is also apparent from Fig. 30. 
As the distance between the eye-piece and objective is practically pre- 
scribed, the shorter the focal length of the ocular the smaller the eye-circle 
and the closer it is to the eye-lens of the ocular. If the diameter of the eye- 
circle be reduced below 0.5 mm. experience has shown that the effects of 
diffraction become serious and practically destroy the definition. This fact 
sets at once a limit to the amount of magnification possible in ordinary micro- 
scopes. With a given objective of definite numerical aperture, the highest 
power ocular which it is possible to use is one which furnishes an eye-point 
at least i mm. in diameter. Of two objectives of the same focal length, 
but of different numerical apertures, the objective with the higher numerical 
aperture (larger rear aperture diafram) will furnish the larger eye-circle 
and thus permit the use of a higher power ocular. When the diameter of 
the eye-circle becomes much less than i mm. shadows from dust particles 
on the eye and irregularities in the eye-lens become prominent and obstruct 
clear vision. For satisfactory work it is essential, therefore, that oculars 
of not too high power be used ; the diameter of the eye-circle should not be 
larger than that of the pupil of the eye and not smaller than about i mm.; 
it should be located at some distance back of the eye-lens of the ocular in 
order that the eye-lashes may not brush against the ocular. 
The diameter of the eye-circle can be readily calculated by the equations 
given above. The eye-circle C'" D'" is theconjugate image of the aperture 
C"D" (Fig. 30). As the focal length of the objective is small compared 
with the tube length of the microscope, the distance of aperture C"D" from 
the lower focal point of the ocular is approximately D of equation (n); 
accordingly 
\C"D" ^D 
\C"'D'" f t 
But the ratio of half the rear aperture objective diafram to the focal length 
\C"D" 
equals approximately the numerical aperture a or - - = a. Therefore 
/ / 
/i/j , 
' a= - tt = 
/ x 
where \' is the magnifying power and/ the focal length of the microscope. 
Tin- equation states that the radius of the Ramsden disk varies directly 
with the numerical aperture and inversely with the magnification. If the 
numerical aperture of the objective be known, the total magnification of 
the microscope can be obtained directly by measuring the diameter of the 
eye-circle. 
