Question

Visitors at a science museum are invited to sit in a chair to the right of a full-length diverging lens (f1 = -3.30 m) and observe a friend sitting in a second chair, 1.80 m to the left of the lens. The visitor then presses a button and a converging lens (f2 = +4.50 m) rises from the floor to a position 2.10 m to the right of the diverging lens, allowing the visitor to view the friend through both lenses at once. Find (a) the magnification of the friend when viewed through the diverging lens only and (b) the overall magnification of the friend when viewed through both lenses. Be sure to include the algebraic sign (+ or -) with your answers.

Answer 1

From lens formula

                   1/f1 = 1/p1 + 1/q1

      then the image distance

               q1 = f p1 / p1 - f1

                     = (-3.3)(1.8) / 1.8 + 3.3

                     = - 1.165 cm

then the magnification M1 = - q1/p1

                         

                                        = - (-1.165) / 1.8 = 0.647

and now the object distance for converging lens is

              p2 = 2.1 + 1.165 = 3.265 cm

   gain from lens formula

            1/f2 = 1/p2 + 1/q2

then the image distance

                  q2 = f 2 p2 / p2 - f2

                       = (4.50)(3.265) / 3.265 - 4.50

                       = -11.90 cm

then the magnification M2 = - (-11.90) / 3.265 = 3.64

Therefore the overall magnification

                 M = M1 M2 = (0.647)(3.64) = 2.355