A telephoto lens system obtains a large magnification in

Chapter 33, Problem 33.108

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A telephoto lens system obtains a large magnification in acompact package. A simple such system can be constructedout of two lenses, one converging and one diverging, offocal lengths f\ and f2 = ~ \ f \, respectively, separatedby a distance i = \ f i as shown in Fig. 33-51.(a) For a distant object located at distance d0 from thefirst lens, show that the first lens forms an image withmagnification mi f i /d Q located very close to its focalpoint. Go on to show that the total magnification for thetwo-lens system is m & 2f \ /d Q. (b) For an object locatedat infinity, show that the two-lens system forms an imagethat is a distance f fi behind the first lens, (c) A single 250-mm-focal-length lens would have to be mountedabout 250 mm from a cameras film in order to producean image of a distant object at d0 with magnification-(250 m m )/dQ. To produce an image of this object withthe same magnification using the two-lens system, whatvalue of fi should be used and how far in front of the filmshould the first lens be placed? How much smaller is the focusing length (i.e., first lens-to-final image distance) ofthis two-lens system in comparison with the 250-mm focusing length of the equivalent single lens?FIGURE 33-51 108.