THE MICROSCOPE AND MICROSCOPIC METHODS IQ 



rays proceeding from the object. It will further be perceived 

 that the sine of the angle of divergence of the beam proceeding, 

 from the object varies directly with the magnification achieved, 

 and further that the magnification in any such system is equal 

 to the quotient of the sine 1 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 intermediate 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 ren- 

 dered parallel, or approximately so, by the first lens. This is the 

 arrangement which exists in the simple microscope or in the ordi- 

 nary reading glass. The magnification achieved by such a simple 

 microscope is measured by the relation between the magnitude 

 of the image 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 con- 

 siderations of magnification, in conditions of hyperopia and pres- 

 byopia 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 refracting media of the presbyopic eye to bring them 

 to a focus. 



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. 



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

 angles designated, rather than the sines. 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. 



