Two lenses, with 1 = +20.0 cm and 2 = + 30.0 cm, are placed on the x axis, as shown in FIGURE 27-28. An

Two lenses, with Æ’1 = +20.0 cm and Æ’2 = + 30.0 cm, are placed on the x axis, as shown in FIGURE 27-28. An object is fixed 50.0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to lens 2 for the following cases:

In figure 27-28

(a) x = 115 cm;
(b) x = 30.0 cm;
(c) x = 0.
(d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, 1/Æ’eff = 1/Æ’1 + 1/Æ’2.

-50.0 cm Image 2 Image 1 Image -115 cm