MAGNIFYING GLASSES. 339 



diminished if less. The first case corresponds with the use of the 

 convex lens in the magic lantern (Expt. 368), the second with that 

 in the camera obscura (Expt. 370). When the object and image 

 are equidistant from the lens each is at a distance equal to twice 

 the focal length (the distance of the geometrical focus from the 

 centre of the lens), on which circumstance is based a simple 

 method of determining the focal length of a convex lens (Expt. 

 369). Just as with mirrors, a simple algebraic formula connects 

 the mutual relationships to one another of the geometrical focus and 

 the situations of any pair of given points forming conjugate foci.* 

 Expt. 367. Simple Microscopes or Magnifying Glasses. A 

 globular smooth transparent bead of glass, a drop of water, or any 

 other convex lenticular (lens-shaped) transparent medium con- 

 stitutes a more or less powerful magnifying glass, according as its 

 focal length (the distance of the centre of the lens from the 

 principal focus) is smaller or greater ; thus a small drop of water 

 hanging from a plate of glass forms a strongly magnifying convexo 

 plane lens. To produce the effect of an ordinary magnifier, how- 

 ever, it is indispensable that the object should be placed at a less 

 distance from the lens than its focal length, in which case the 

 image is virtual and erect. Fig. 

 186 represents the formation of 

 an image, ab, thus seen by an 

 observer at 0. The amount of 

 linear magnification is expressed 

 by the ratio of the angle aOb, 

 subtended by the image at the 

 eye, to A0l{ that subtended by 

 the object ; this ratio may be made 

 greater than 100 to 1 with a suitable lens; i.e., the object becomes 



* This formula is the same as that for mirrors, viz. : 



1 1 1 



*+y = r 



x being the distance of the object from the lens (regarded as of negligible 

 thickness), y that of the image, and/ that of the geometrical focus. These 

 latter two distances are considered as + or- according as they are measured 

 from the mirror in the same direction as x, or in the opposite direction. In- 

 the case of a lens, as the rays must pass through it to form a real image, such 

 an image can only be formed when x and y are opposite in sign; i.e., when 

 y is - ; and for the same reason the value of/ (when the sun or other bright 

 object from which the light emanates is regarded as at an infinite distance) 

 is- for a convex lens, and + for a concave one. Hence, in the case of 

 a concave lens (fig. 185), x, y, and/ are all three of the same sign, i.e., y and/ 

 are+ ; with a convex lens used as a magnifying glass (fig. 183), y is + and/- ; 

 and when used as either a magic lantern or camera obscura, both y and/ are 

 (tig. 187). 



