40 THEORY OF THE MICROSCOPE. 



field-lens by the relation already given, -- + ^ = -- > in which, 



P P* f 



in accordance with former assumptions regarding the tube-length 

 and the position of the principal points, p = 200 (48 + 24011) 

 = 149-5989, and / = 40 mm. We get p* = 54-598 mm., and 

 since we regard the point determined b} r it as the virtual object of 

 the eye-lens, the calculation gives as abscissa-value of the final 

 real image-point, N* + 5*938, where N* is the last refracting 

 surface of the eye-piece. 



The axes of the pencils, which correspond to the different points 

 of the object, all intersect therefore in one point, which lies about 

 6 mm. above the eye-lens. This point may be termed the eye-point. 

 A plane drawn through it perpendicular to the axis will, in general, 

 be cut by each separate pencil of light in an ellipse ; the whole 

 cone of pencils, however, cuts the axes in a circle, the diameter of 

 which, with given optical constants, depends upon the angle of 

 aperture of the Microscope. If the latter is, say, 60, the former 

 will be somewhat greater than J mm. ; both increase and decrease 

 simultaneously. As the diameter of the pupil of the eye is con- 

 siderably larger, it is evident that it need not necessarily be 

 brought to the eye-point, but merely in proximity to it, in order 

 that all the rays of the emergent pencils of light may reach the 

 retina. 



Since the eye-point coincides within a small fraction of a milli- 

 metre with the second focal point, its position is obviously indicated 

 by the real image of the source of light, which is formed above 

 the eye-piece. If, for instance, we employ as source of light a 

 window close at hand, or its image in the mirror of the Microscope, 

 we see in the plane of the eye-point, with a suitable adjustment of 

 the mirror, the clearly defined diminutive image of the window- 

 frame or other objects which lie in the region of the effective rays. 

 The diameter of this image, which may easily be determined by 

 the method of construction applied in Fig. 8, corresponds therefore 

 to the smallest transverse section of the emergent pencil of rays in 

 the plane of the eye-point, or, otherwise expressed, the transverse 

 section in question is given by the aperture-image above the eye- 

 piece. We are now in a position to work out the construction of 

 this image for a particular case with the constants above found, 

 and, at the same time, to illustrate by a diagram the connection 

 between the angle of aperture and the size of the image-surface. 



