108 



THEORY OF THE MICROSCOPE 



If a convex lens of focal length 2 in. be placed 2 in. in front of an object AB 

 (fig. 100), the divergent pencil of light from A, HAO, will emerge from the lens as a 

 parallel beam F"H, LO, as if it came from an object A' at an infinite distance off, 

 while the divergent pencil of rays from B will emerge from the lens as a beam parallel 

 to the axis, as if it came from B' at an infinite distance off. The image is virtual, 



FIG. 100. 



not real, and cannot therefore be received on a ground-glass screen, but it appears 

 to the eye as if it came from a big object at an enormous distance away. 



The visual angle which this huge image at an infinite distance subtends at the 

 eye will obviously be BOA or 0', and 



BA BA 

 "-/'' 



tan #' = TS^,= 



OB - 



But 



tan f ; 



tan 



I 10 



The object is therefore magnified 5 times by the convex lens of 2 in. focal length 

 placed 2 in. from it. The positive sign shows that the image is erect and virtual. 



Now suppose it be required to magnify an object 10 times (linear) it is clear 

 that a lens of 1 in. focal length would have to be used, for 



10 10 



and to obtain a magnification of 400 it would be necessary to have a lens of focal 

 length j\j in., and the object would therefore have to be not more than ^ in. away 

 from the lens ; this in most cases would be impossible, not to speak of the extreme 

 spherical and chromatic aberration that would be induced by using a single lens of 

 that high degree of curvature. 



There is a simple method by which some of these defects may be overcome, which 

 may be illustrated by a consideration of the simple magnifying glass of 1 in. focal 

 length mentioned above. In this case the lens must be placed 1 in. away from 

 the object to induce a magnification of ten diameters. Now if this biconvex 

 lens be split down the middle, two plano-convex lenses will be formed each of 2 in. 

 focal length. On placing one of these lenses 2 in. away from the object AB, an 

 enlarged inverted image ab will be formed at a distance of 18 in. from the lens 

 (fig. 101). 



(For H4 ; ':H~f^~r-is ; ?=- 18in - 



where p is the distance from the object and q the distance from the image to the 

 lens, and / the focal length of the lens. ) 



On now placing the second plano-convex lens 2 in. beyond this image (i.e. 

 with the image at its focal distance, it will be magnified again. This is the funda- 



