OCULARS. 



25 



length of Ve inch. The Vis incn objective has two single lenses 

 and two doublets. The compound lenses in the pieces serve the 

 purpose of correcting aberration defects. The objectives are 

 achromatic. 



ANGULAR APERTURE OF A LENS. The efficiency of an objective 

 is in great part dependent upon the size of the cone of light it 

 can take in from a point of the object to form its image. The 

 cone of light utilized is approximately measured by the so-called 

 angular aperture. For a single lens this is the angle formed 

 by lines joining the focal point with the edges of the lens. In 

 an objective it is the angle formed by the lines from the focal 

 point to the edges of the uppermost lens of the system. More 

 accurately, the cone of light utilized is measured by the product 

 of the index of refraction of the medium between the objective 

 and the cover-glass lying over the object, and the sine of half 

 the angular aperture, which is expressed thus, n. sine u, where 

 n is the index of refraction and u is half the angular aperture. 

 This expression is known as the numerical aperture. In the 

 case of dry objectives n is one (index of refraction of air) ; for 

 water-immersion objectives n is 1.33 ; for cedar-oil immersion 

 objectives n is 1.52. It will be seen that the cone of light that 

 can be utilized by an objective of a given angular aperture is 

 considerably greater for an immersion lens than for a dry lens. 

 As the angular aperture varies inversely as the focal length, it 

 follows that the shorter the focal length is the greater is the 

 cone of light that the lens can utilize ; in other words, lenses of 

 high magnification can utilize a greater cone of light than those 

 of low magnification. 



OCULARS OR EYE-PIECES. The Huyghens' eye-piece is univer- 

 sally used. It is known as a negative eye-piece. Its construc- 

 tion is shown in Fig. 25, which consists of 

 two plano-convex crown lenses, the lower one 

 being the larger, less magnifying (its focal 

 length being three times that of the upper 

 lens). It is known as the field lens. It in- 

 creases the field of vision, i. e., the number 

 of points of the object that are made visible 

 through the instrument. The upper lens is 

 known as the eye lens. It magnifies the 

 image formed by the objective. Both lenses 

 have their convex surfaces turned towards 

 the object. Midway between them is a per- 

 forated diaphragm, the object of which is to 

 cut out edge rays from the image and thus 

 decrease spherical aberration. The virtues 

 of the Huyghens' eye-piece are that it corrects chromatic aber- 

 ration, enlarges the field of vision and forms a flat image, i. e., 



