THE mCEOSCOPE AND MICROSCOPIC METHODS IQ 



that the magnification in any such system is equal to the quotient 

 of the sine^ of the angle of divergence of the beam proceeding from 

 the object, divided by the sine of the angle of convergence of the 

 beam to form the image. This is capable of mathematical proof 

 and is illustrated in the four figures. From these it is evident that 

 magnification is a function of the relation of these two angles of 

 the opening and closing limbs of the beam, and that the inter- 

 mediate course of the rays, whether parallel, convergent or 

 divergent, is negligible in this computation. If the second lens 

 be that of the eye and an image is to be formed on the retina, then 

 the rays proceeding from a point must be rendered parallel, or 

 approximately so, by the first lens. This is the arrangement 

 which exists in the simple microscope or in the ordinary reading 

 glass. The magnification achieved by such a simple microscope 

 is measured by the relation between the magnitude of the :'mage 

 on the retina when the lens is employed, and the size of' such an 

 image when the lens is left out of the path of the light. The 

 value of the reading glass, entirely aside from considerations of 

 magnification, in conditions of hyperopia and presbyopia is also 

 evident from these figures, as it of course renders the rays coming 

 from a near point more nearly parallel, and thus enables the re- 

 fracting media of the presbyopic eye to bring them to a focu^. 



So far we have been employing in our discussion the ideal lens, 

 one which refracts all light equally and brings to a focus in one 

 plane all rays proceeding from one plane in the object. As 

 a matter of fact the ideal lens in this sense does not exist. The 

 simple convex lens has many serious optical defects. 



Points in the same plane in the object are imaged by the simple 

 lens on a curved surface, the segment of a spherical surface. 

 This defect is known as spherical aberration. It is diminished 

 to some extent by combining convex and concave lenses and the 



'In the figures, as drawn, this statement actually applies to the tangents of the 

 angles designated, rather than the sinp. However, for very small angles the sine 

 and tangent are approximately equal. The use of the term sine finds its complete 

 justification in the fact that the plane at which the rays are bent is not flat but is 

 the segment of a sphere or its optical equivalent. 



