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48       LENSES AND GEOMETRICAL OPTICS


                                                                                           a < f
                                                F                   F
                                                                                           Virtual
                                       Image     Object                                    magnified
                                                                                           image
                                                      a
                                                                 (a)

                                 No image      F


                                                                    F                      a = f
                                                                                           Image
                                             Object                                        distance ∞
                                                     a
                                                                 (b)




                                               F                   F               Image   2f > a > f
                                                                                           Real magnified
                                           Object                                          image
                                                   a

                                                                 (c)


                                                                    F         2F           a = 2f
                                                                                           Real,
                                      2F
                                                F                                          magnified = 1x
                                                a

                                                                 (d)


                                                                   F   Image               a > 2f
                                                                                           Real,
                                Object          F                                          demagnified
                                              a
                                                                 (e)

                                Figure 4-6
                                Object-image relationships. (a) a   f; (b) a   f; (c) 2f   a   f; (d) a   2f; (e) a   2f.



                                the image may be real or virtual, and either magnified or demagnified (Fig. 4-6;
                                Spencer, 1982). It is good practice to work through the following relationships using any
                                handheld magnifier or simple biconvex lens such as the front lens of a binocular (10–50
                                mm is convenient), whose focal length has been determined by the procedure just
                                described. The object should be self-luminous, moderately bright, and well defined. A
                                5–10 mm diameter hole cut in a large opaque cardboard sheet placed in front of a lamp
                                works well as an object. Work in a partially darkened room. It is useful to remember the
                                principal conditions describing object-image relationships for a simple positive lens:
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